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test_values.html
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<html>
<head>
<title>
TEST_VALUES - Sample Function Values
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_VALUES <br> Sample Function Values
</h1>
<hr>
<p>
<b>TEST_VALUES</b>
is a FORTRAN90 library which
stores a few selected values of various mathematical functions.
</p>
<p>
The intent of <b>TEST_VALUES</b> is to provide a means of making
very simple tests for correctness of software designed to compute
a variety of functions. The testing can be done automatically.
The data provided is generally skimpy, and might not test the
algorithm over a suitably wide range. It does, however, provide
a small amount of reassurance that a given computation is (or
is not) computing the appropriate quantity, and doing so
reasonably accurately.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TEST_VALUES</b> is available in
<a href = "../../c_src/test_values/test_values.html">a C version</a> and
<a href = "../../cpp_src/test_values/test_values.html">a C++ version</a> and
<a href = "../../f77_src/test_values/test_values.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_values/test_values.html">a FORTRAN90 version</a> and
<a href = "../../math_src/test_values/test_values.html">a MATHEMATICA version</a> and
<a href = "../../m_src/test_values/test_values.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Programs:
</h3>
<p>
<a href = "../../f_src/cordic/cordic.html">
CORDIC</a>,
a FORTRAN90 library which
use the CORDIC method to compute certain elementary functions.
</p>
<p>
<a href = "../../f_src/fn/fn.html">
FN</a>,
a FORTRAN90 library which
evaluates elementary and special functions,
by Wayne Fullerton.
</p>
<p>
<a href = "../../cpp_src/gsl/gsl.html">
GSL</a>,
a C++ library which
is known as the Gnu Scientific Library,
and evaluates many special functions.
</p>
<p>
<a href = "../../f_src/polpak/polpak.html">
POLPAK</a>,
a FORTRAN90 library which
computes various mathematical functions;
test values for many of these functions are available in
TEST_VALUES.
</p>
<p>
<a href = "../../f_src/prob/prob.html">
PROB</a>,
a FORTRAN90 library which
computes various statistical functions;
test values for many of these functions are available in TEST_VALUES.
</p>
<p>
<a href = "../../f_src/specfun/specfun.html">
SPECFUN</a>,
a FORTRAN90 library which
computes various special functions, particularly Bessel functions.
</p>
<p>
<a href = "../../f_src/special_functions/special_functions.html">
SPECIAL_FUNCTIONS</a>,
a FORTRAN90 library which
computes special functions,
by Shanjie Zhang, Jianming Jin;
</p>
<p>
<a href = "../../f_src/steam/steam.html">
STEAM</a>,
a FORTRAN90 library which
computes various functions related
to the physical properties of water; test values for many of these
functions are available in TEST_VALUES.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Milton Abramowitz, Irene Stegun,<br>
Handbook of Mathematical Functions,<br>
National Bureau of Standards, 1964,<br>
ISBN: 0-486-61272-4,<br>
LC: QA47.A34.
</li>
<li>
Robert Corless, Gaston Gonnet, David Hare, David Jeffrey,
Donald Knuth,<br>
On the Lambert W Function,<br>
Advances in Computational Mathematics,<br>
Volume 5, 1996, pages 329-359.
</li>
<li>
Gerard Cornuejols, Regina Urbaniak, Robert Weismantel, Laurence Wolsey,<br>
Decomposition of Integer Programs and of Generating Sets,<br>
in Algorithms - ESA '97,<br>
Lecture Notes in Computer Science 1284,<br>
edited by R Burkard, G Woeginger,<br>
Springer, 1997, pages 92-103,<br>
LC: QA76.9.A43.E83.
</li>
<li>
Marc Deleglise, Joel Rivat,<br>
Computing the Summation of the Moebius Function,<br>
Experimental Mathematics,<br>
Volume 5, 1996, pages 291-295.
</li>
<li>
Lester Haar, John Gallagher, George Kell,<br>
NBS/NRC Steam Tables:<br>
Thermodynamic and Transport Properties and Computer Programs
for Vapor and Liquid States of Water in SI Units,<br>
Hemisphere Publishing Corporation, Washington, 1984,<br>
ISBN: 0-89116-353-0,<br>
LC: TJ270.H3.
</li>
<li>
Brian Hayes,<br>
"Why W?",<br>
The American Scientist,<br>
Volume 93, March-April 2005, pages 104-108.
</li>
<li>
Kanti Mardia, Peter Jupp,<br>
Directional Statistics,<br>
Wiley, 2000,<br>
ISBN: 0471953334,<br>
LC: QA276.M335
</li>
<li>
Allan McLeod,<br>
Algorithm 757:
MISCFUN: A software package to compute uncommon
special functions,<br>
ACM Transactions on Mathematical Software,<br>
Volume 22, Number 3, September 1996, pages 288-301.
</li>
<li>
National Bureau of Standards, <br>
Tables of the Bivariate Normal Distribution and Related Functions,<br>
Applied Mathematics Series, Number 50, 1959.
</li>
<li>
Robert Owens,<br>
An Algorithm to Solve the Frobenius Problem,<br>
Mathematics Magazine,<br>
Volume 76, Number 4, October 2003, 264-275.
</li>
<li>
Karl Pearson,<br>
Tables of the Incomplete Beta Function,<br>
Cambridge University Press, 1968,<br>
ISBN: 0521059224,<br>
LC: QA351.P38.
</li>
<li>
Frank Powell,<br>
Statistical Tables for Sociology, Biology and Physical Sciences,<br>
Cambridge University Press, 1982,<br>
ISBN: 0521284732,<br>
LC: QA276.25.S73.
</li>
<li>
Edward Reingold, Nachum Dershowitz,<br>
Calendrical Calculations: The Millennium Edition,<br>
Cambridge University Press, 2001,<br>
ISBN: 0-521-77752-6,<br>
LC: CE12.R45.
</li>
<li>
Johannes van der Corput,<br>
Verteilungsfunktionen,<br>
Proc Akad Amsterdam,<br>
Volume 38, 1935, <br>
Volume 39, 1936.
</li>
<li>
Eric Weisstein,<br>
CRC Concise Encyclopedia of Mathematics,<br>
CRC Press, 2002,<br>
Second edition,<br>
ISBN: 1584883472,<br>
LC: QA5.W45
</li>
<li>
Stephen Wolfram,<br>
The Mathematica Book,<br>
Fourth Edition,<br>
Cambridge University Press, 1999,<br>
ISBN: 0-521-64314-7,<br>
LC: QA76.95.W65.
</li>
<li>
Shanjie Zhang, Jianming Jin,<br>
Computation of Special Functions,<br>
Wiley, 1996,<br>
ISBN: 0-471-11963-6,<br>
LC: QA351.C45.
</li>
<li>
Daniel Zwillinger, editor,<br>
CRC Standard Mathematical Tables and Formulae,<br>
30th Edition,<br>
CRC Press, 1996,<br>
ISBN: 0-8493-2479-3,<br>
LC: QA47.M315.
</li>
<li>
Daniel Zwillinger, Steven Kokoska,<br>
Standard Probability and Statistical Tables,<br>
CRC Press, 2000,<br>
ISBN: 1-58488-059-7,<br>
LC: QA273.3.Z95.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_values.f90">test_values.f90</a>, the source code.
</li>
<li>
<a href = "test_values.sh">test_values.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_values_prb.f90">test_values_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "test_values_prb.sh">test_values_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "test_values_prb_output.txt">
test_values_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ABRAM0_VALUES</b> returns some values of the Abramowitz0 function.
</li>
<li>
<b>ABRAM1_VALUES</b> returns some values of the Abramowitz1 function.
</li>
<li>
<b>ABRAM2_VALUES</b> returns some values of the Abramowitz2 function.
</li>
<li>
<b>AGM_VALUES</b> returns some values of the AGM.
</li>
<li>
<b>AIRY_AI_VALUES</b> returns some values of the Airy Ai(x) function.
</li>
<li>
<b>AIRY_AI_INT_VALUES</b> returns some values of the integral of the Airy function.
</li>
<li>
<b>AIRY_AI_PRIME_VALUES</b> returns some values of the Airy function Ai'(x).
</li>
<li>
<b>AIRY_BI_VALUES</b> returns some values of the Airy Bi(x) function.
</li>
<li>
<b>AIRY_BI_INT_VALUES</b> returns some values of the integral of the Airy function.
</li>
<li>
<b>AIRY_BI_PRIME_VALUES</b> returns some values of the Airy function Bi'(x).
</li>
<li>
<b>AIRY_CAI_VALUES</b> returns some values of the Airy Ai(x) with complex argument.
</li>
<li>
<b>AIRY_CBI_VALUES</b> returns some values of the Airy Bi(x) with complex argument.
</li>
<li>
<b>AIRY_GI_VALUES</b> returns some values of the Airy Gi function.
</li>
<li>
<b>AIRY_HI_VALUES</b> returns some values of the Airy Hi function.
</li>
<li>
<b>ARCCOS_VALUES</b> returns some values of the arc cosine function.
</li>
<li>
<b>ARCCOSH_VALUES</b> returns some values of the hyperbolic arc cosine function.
</li>
<li>
<b>ARCSIN_VALUES</b> returns some values of the arc sine function.
</li>
<li>
<b>ARCSINH_VALUES</b> returns some values of the hyperbolic arc sine function.
</li>
<li>
<b>ARCTAN_VALUES</b> returns some values of the arc tangent function.
</li>
<li>
<b>ARCTAN_INT_VALUES</b> returns some values of the inverse tangent integral.
</li>
<li>
<b>ARCTAN2_VALUES:</b> arc tangent function of two arguments.
</li>
<li>
<b>ARCTANH_VALUES</b> returns some values of the hyperbolic arc tangent function.
</li>
<li>
<b>BEI0_VALUES</b> returns some values of the Kelvin BEI function of order NU = 0.
</li>
<li>
<b>BEI1_VALUES</b> returns some values of the Kelvin BEI function of order NU = 1.
</li>
<li>
<b>BELL_VALUES</b> returns some values of the Bell numbers.
</li>
<li>
<b>BER0_VALUES</b> returns some values of the Kelvin BER function of order NU = 0.
</li>
<li>
<b>BER1_VALUES</b> returns some values of the Kelvin BER function of order NU = 1.
</li>
<li>
<b>BERNOULLI_NUMBER_VALUES</b> returns some values of the Bernoulli numbers.
</li>
<li>
<b>BERNOULLI_POLY_VALUES</b> returns some values of the Bernoulli polynomials.
</li>
<li>
<b>BERNSTEIN_POLY_VALUES</b> returns some values of the Bernstein polynomials.
</li>
<li>
<b>BESSEL_I0_INT_VALUES</b> returns some values of the Bessel I0 integral.
</li>
<li>
<b>BESSEL_I0_SPHERICAL_VALUES:</b> some values of the Spherical Bessel function i0.
</li>
<li>
<b>BESSEL_I0_VALUES</b> returns some values of the I0 Bessel function.
</li>
<li>
<b>BESSEL_I1_SPHERICAL_VALUES:</b> some values of the Spherical Bessel function i1.
</li>
<li>
<b>BESSEL_I1_VALUES</b> returns some values of the I1 Bessel function.
</li>
<li>
<b>BESSEL_IN_VALUES</b> returns some values of the In Bessel function.
</li>
<li>
<b>BESSEL_IX_VALUES</b> returns some values of the Ix Bessel function.
</li>
<li>
<b>BESSEL_J0_INT_VALUES</b> returns some values of the Bessel J0 integral.
</li>
<li>
<b>BESSEL_J0_SPHERICAL_VALUES:</b> some values of the Spherical Bessel function j0.
</li>
<li>
<b>BESSEL_J0_VALUES</b> returns some values of the J0 Bessel function.
</li>
<li>
<b>BESSEL_J1_SPHERICAL_VALUES:</b> some values of the Spherical Bessel function j1.
</li>
<li>
<b>BESSEL_J1_VALUES</b> returns some values of the J1 Bessel function.
</li>
<li>
<b>BESSEL_JN_VALUES</b> returns some values of the Jn Bessel function.
</li>
<li>
<b>BESSEL_JX_VALUES</b> returns some values of the Jx Bessel function.
</li>
<li>
<b>BESSEL_K0_VALUES</b> returns some values of the K0 Bessel function.
</li>
<li>
<b>BESSEL_K0_INT_VALUES</b> returns some values of the Bessel K0 integral.
</li>
<li>
<b>BESSEL_K1_VALUES</b> returns some values of the K1 Bessel function.
</li>
<li>
<b>BESSEL_KN_VALUES</b> returns some values of the Kn Bessel function.
</li>
<li>
<b>BESSEL_KX_VALUES</b> returns some values of the Kx Bessel function.
</li>
<li>
<b>BESSEL_Y0_VALUES</b> returns some values of the Y0 Bessel function.
</li>
<li>
<b>BESSEL_Y0_INT_VALUES</b> returns some values of the Bessel Y0 integral.
</li>
<li>
<b>BESSEL_Y0_SPHERICAL_VALUES:</b> some values of the Spherical Bessel function y0.
</li>
<li>
<b>BESSEL_Y1_VALUES</b> returns some values of the Y1 Bessel function.
</li>
<li>
<b>BESSEL_Y1_SPHERICAL_VALUES:</b> some values of the Spherical Bessel function y1.
</li>
<li>
<b>BESSEL_YN_VALUES</b> returns some values of the Yn Bessel function.
</li>
<li>
<b>BESSEL_YX_VALUES</b> returns some values of the Yx Bessel function.
</li>
<li>
<b>BETA_CDF_VALUES</b> returns some values of the Beta CDF.
</li>
<li>
<b>BETA_INC_VALUES</b> returns some values of the incomplete Beta function.
</li>
<li>
<b>BETA_LOG_VALUES</b> returns some values of the logarithm of the Beta function.
</li>
<li>
<b>BETA_NONCENTRAL_CDF_VALUES</b> returns some values of the noncentral Beta CDF.
</li>
<li>
<b>BETA_VALUES</b> returns some values of the Beta function.
</li>
<li>
<b>BINOMIAL_VALUES</b> returns some values of the binomial coefficients.
</li>
<li>
<b>BINOMIAL_CDF_VALUES</b> returns some values of the binomial CDF.
</li>
<li>
<b>BIVARIATE_NORMAL_CDF_VALUES</b> returns some values of the bivariate normal CDF.
</li>
<li>
<b>CATALAN_VALUES</b> returns some values of the Catalan numbers.
</li>
<li>
<b>CAUCHY_CDF_VALUES</b> returns some values of the Cauchy CDF.
</li>
<li>
<b>CBRT_VALUES</b> returns some values of the cube root function.
</li>
<li>
<b>CHEBY_T_POLY_VALUES</b> returns values of the Chebyshev T polynomial.
</li>
<li>
<b>CHEBY_U_POLY_VALUES</b> returns values of the Chebyshev U polynomial.
</li>
<li>
<b>CHI_VALUES</b> returns some values of the hyperbolic cosine integral function.
</li>
<li>
<b>CHI_SQUARE_CDF_VALUES</b> returns some values of the Chi-Square CDF.
</li>
<li>
<b>CHI_SQUARE_NONCENTRAL_CDF_VALUES</b> returns values of the noncentral chi CDF.
</li>
<li>
<b>CI_VALUES</b> returns some values of the cosine integral function.
</li>
<li>
<b>CIN_VALUES</b> returns some values of the alternate cosine integral function.
</li>
<li>
<b>CINH_VALUES</b> returns some values of the alternate hyperbolic cosine integral.
</li>
<li>
<b>CLAUSEN_VALUES</b> returns some values of the Clausen's integral.
</li>
<li>
<b>CLEBSCH_GORDAN_VALUES</b> returns some values of the Clebsch-Gordan function.
</li>
<li>
<b>COLLATZ_COUNT_VALUES</b> returns some values of the Collatz count function.
</li>
<li>
<b>COS_VALUES</b> returns some values of the cosine function.
</li>
<li>
<b>COSH_VALUES</b> returns some values of the hyperbolic cosine function.
</li>
<li>
<b>COT_VALUES</b> returns some values of the cotangent function.
</li>
<li>
<b>CP_VALUES</b> returns some values of the specific heat at constant pressure.
</li>
<li>
<b>DAWSON_VALUES</b> returns some values of Dawson's integral.
</li>
<li>
<b>DEBYE1_VALUES</b> returns some values of Debye's function of order 1.
</li>
<li>
<b>DEBYE2_VALUES</b> returns some values of Debye's function of order 2.
</li>
<li>
<b>DEBYE3_VALUES</b> returns some values of Debye's function of order 3.
</li>
<li>
<b>DEBYE4_VALUES</b> returns some values of Debye's function of order 4.
</li>
<li>
<b>DEDEKIND_SUM_VALUES</b> returns some values of the Dedekind sum.
</li>
<li>
<b>DIELECTRIC_VALUES</b> returns some values of the static dielectric constant.
</li>
<li>
<b>DILOGARITHM_VALUES</b> returns some values of the dilogarithm function.
</li>
<li>
<b>E1_VALUES</b> returns some values of the exponential integral function E1(X).
</li>
<li>
<b>EI_VALUES</b> returns some values of the exponential integral function EI(X).
</li>
<li>
<b>ELLIPTIC_EA_VALUES</b> returns values of the complete elliptic integral E(ALPHA).
</li>
<li>
<b>ELLIPTIC_EM_VALUES</b> returns values of the complete elliptic integral E(M).
</li>
<li>
<b>ELLIPTIC_KA_VALUES</b> returns values of the complete elliptic integral K(ALPHA).
</li>
<li>
<b>ELLIPTIC_KM_VALUES</b> returns values of the complete elliptic integral K(M).
</li>
<li>
<b>ERF_VALUES</b> returns some values of the ERF or "error" function.
</li>
<li>
<b>ERFC_VALUES</b> returns some values of the complementary error function.
</li>
<li>
<b>EULER_NUMBER_VALUES</b> returns some values of the Euler numbers.
</li>
<li>
<b>EULER_POLY_VALUES</b> returns some values of the Euler polynomials.
</li>
<li>
<b>EXP_VALUES</b> returns some values of the exponential function.
</li>
<li>
<b>EXP3_INT_VALUES</b> returns some values of the EXP3 integral function.
</li>
<li>
<b>EXPONENTIAL_CDF_VALUES</b> returns some values of the Exponential CDF.
</li>
<li>
<b>EXTREME_VALUES_CDF_VALUES</b> returns some values of the Extreme Values CDF.
</li>
<li>
<b>F_CDF_VALUES</b> returns some values of the F CDF test function.
</li>
<li>
<b>F_NONCENTRAL_CDF_VALUES</b> returns some values of the F CDF test function.
</li>
<li>
<b>FACTORIAL_RISING_VALUES</b> returns values of the integer Pochhammer function.
</li>
<li>
<b>FACTORIAL_VALUES</b> returns values of the factorial function.
</li>
<li>
<b>FACTORIAL2_VALUES</b> returns values of the double factorial function.
</li>
<li>
<b>FRESNEL_COS_VALUES</b> returns values of the Fresnel cosine integral function.
</li>
<li>
<b>FRESNEL_SIN_VALUES</b> returns some values of the Fresnel sine integral function.
</li>
<li>
<b>FROBENIUS_NUMBER_DATA_VALUES</b> returns data for the Frobenius problem.
</li>
<li>
<b>FROBENIUS_NUMBER_ORDER_VALUES</b> returns orders of the Frobenius problem.
</li>
<li>
<b>FROBENIUS_NUMBER_ORDER2_VALUES:</b> some values of the order 2 Frobenius number.
</li>
<li>
<b>GAMMA_VALUES</b> returns some values of the Gamma function.
</li>
<li>
<b>GAMMA_CDF_VALUES</b> returns some values of the Gamma CDF.
</li>
<li>
<b>GAMMA_INC_P_VALUES:</b> values of normalized incomplete Gamma function P(A,X).
</li>
<li>
<b>GAMMA_INC_Q_VALUES:</b> values the normalized incomplete Gamma function Q(A,X).
</li>
<li>
<b>GAMMA_INC_TRICOMI_VALUES:</b> Tricomi's incomplete Gamma function.
</li>
<li>
<b>GAMMA_INC_VALUES:</b> values of the incomplete Gamma function.
</li>
<li>
<b>GAMMA_LOG_VALUES</b> returns some values of the Log Gamma function.
</li>
<li>
<b>GEGENBAUER_POLY_VALUES</b> returns some values of the Gegenbauer polynomials.
</li>
<li>
<b>GEOMETRIC_CDF_VALUES</b> returns values of the geometric CDF.
</li>
<li>
<b>GOODWIN_VALUES</b> returns some values of the Goodwin and Staton function.
</li>
<li>
<b>GUD_VALUES</b> returns some values of the Gudermannian function.
</li>
<li>
<b>HERMITE_FUNCTION_VALUES:</b> values of the Hermite function.
</li>
<li>
<b>HERMITE_POLY_PHYS_VALUES:</b> values of the physicist's Hermite polynomial.
</li>
<li>
<b>HERMITE_POLY_PROB_VALUES:</b> values of the probabilist's Hermite polynomial.
</li>
<li>
<b>HYPER_1F1_VALUES</b> returns some values of the hypergeometric function 1F1.
</li>
<li>
<b>HYPER_2F1_VALUES</b> returns some values of the hypergeometric function 2F1.
</li>
<li>
<b>HYPERGEOMETRIC_CDF_VALUES</b> returns some values of the hypergeometric CDF.
</li>
<li>
<b>HYPERGEOMETRIC_PDF_VALUES</b> returns some values of the hypergeometric PDF.
</li>
<li>
<b>HYPERGEOMETRIC_U_VALUES:</b> some values of the hypergeometric function U(a,b,x).
</li>
<li>
<b>I0ML0_VALUES</b> returns some values of the I0ML0 function.
</li>
<li>
<b>I1ML1_VALUES</b> returns some values of the I1ML1 function.
</li>
<li>
<b>INT_VALUES</b> returns some values of the "integer part" function.
</li>
<li>
<b>JACOBI_CN_VALUES</b> returns some values of the Jacobi elliptic function CN(A,X).
</li>
<li>
<b>JACOBI_DN_VALUES</b> returns some values of the Jacobi elliptic function DN(A,X).
</li>
<li>
<b>JACOBI_POLY_VALUES</b> returns some values of the Jacobi polynomial.
</li>
<li>
<b>JACOBI_SN_VALUES</b> returns some values of the Jacobi elliptic function SN(A,X).
</li>
<li>
<b>JED_CE_VALUES</b> returns the Common Era dates for Julian Ephemeris Dates.
</li>
<li>
<b>JED_MJD_VALUES</b> returns the MJD for Julian Ephemeris Dates.
</li>
<li>
<b>JED_RD_VALUES</b> returns the RD for Julian Ephemeris Dates.
</li>
<li>
<b>JED_WEEKDAY_VALUES</b> returns the day of the week for Julian Ephemeris Dates.
</li>
<li>
<b>KEI0_VALUES</b> returns some values of the Kelvin KEI function of order NU = 0.
</li>
<li>
<b>KEI1_VALUES</b> returns some values of the Kelvin KEI function of order NU = 1.
</li>
<li>
<b>KER0_VALUES</b> returns some values of the Kelvin KER function of order NU = 0.
</li>
<li>
<b>KER1_VALUES</b> returns some values of the Kelvin KER function of order NU = 1.
</li>
<li>
<b>LAGUERRE_ASSOCIATED_VALUES</b> returns values of associated Laguerre polynomials.
</li>
<li>
<b>LAGUERRE_GENERAL_VALUES</b> returns values of the generalized Laguerre function.
</li>
<li>
<b>LAGUERRE_POLYNOMIAL_VALUES:</b> some values of the Laguerre polynomial L(n,x).
</li>
<li>
<b>LAMBERT_W_VALUES</b> returns some values of the Lambert W function.
</li>
<li>
<b>LAPLACE_CDF_VALUES</b> returns some values of the Laplace CDF.
</li>
<li>
<b>LEGENDRE_ASSOCIATED_VALUES</b> returns values of associated Legendre functions.
</li>
<li>
<b>LEGENDRE_ASSOCIATED_NORMALIZED_SPHERE_VALUES:</b> normalized associated Legendre.
</li>
<li>
<b>LEGENDRE_ASSOCIATED_NORMALIZED_VALUES:</b> normalized associated Legendre.
</li>
<li>
<b>LEGENDRE_FUNCTION_Q_VALUES</b> returns values of the Legendre Q function.
</li>
<li>
<b>LEGENDRE_POLY_VALUES</b> returns values of the Legendre polynomials.
</li>
<li>
<b>LERCH_VALUES</b> returns some values of the Lerch transcendent function.
</li>
<li>
<b>LINEAR_SYSTEM_VALUES</b> returns some linear systems.
</li>
<li>
<b>LOBACHEVSKY_VALUES</b> returns some values of the Lobachevsky function.
</li>
<li>
<b>LOG_VALUES</b> returns some values of the natural logarithm function.
</li>
<li>
<b>LOG_NORMAL_CDF_VALUES</b> returns some values of the Log Normal CDF.
</li>
<li>
<b>LOG_SERIES_CDF_VALUES</b> returns some values of the log series CDF.
</li>
<li>
<b>LOG10_VALUES</b> returns some values of the logarithm 10 function.
</li>
<li>
<b>LOGARITHMIC_INTEGRAL_VALUES</b> returns values of the logarithmic integral LI(X).
</li>
<li>
<b>LOGISTIC_CDF_VALUES</b> returns some values of the Logistic CDF.
</li>
<li>
<b>MATHIEU_EVEN_VALUES</b> returns eigenvalues of even Mathieu solutions.
</li>
<li>
<b>MATHIEU_ODD_VALUES</b> returns eigenvalues of odd Mathieu solutions.
</li>
<li>
<b>MERTENS_VALUES</b> returns some values of the Mertens function.
</li>
<li>
<b>MOEBIUS_VALUES</b> returns some values of the Moebius function.
</li>
<li>
<b>NEGATIVE_BINOMIAL_CDF_VALUES</b> returns values of the negative binomial CDF.
</li>
<li>
<b>NINE_J_VALUES</b> returns some values of the Wigner 9J function.
</li>
<li>
<b>NORMAL_CDF_VALUES</b> returns some values of the Normal CDF.
</li>
<li>
<b>NORMAL_01_CDF_VALUES</b> returns some values of the Normal 01 CDF.
</li>
<li>
<b>OMEGA_VALUES</b> returns some values of the OMEGA function.
</li>
<li>
<b>OWEN_VALUES</b> returns some values of Owen's T function.
</li>
<li>
<b>PARTITION_COUNT_VALUES</b> returns some values of the integer partition count.
</li>
<li>
<b>PARTITION_DISTINCT_COUNT_VALUES</b> returns some values of Q(N).
</li>
<li>
<b>PHI_VALUES</b> returns some values of the PHI function.
</li>
<li>
<b>PI_VALUES</b> returns values of the Pi function.
</li>
<li>
<b>POCHHAMMER_VALUES</b> returns some values of the Pochhammer function.
</li>
<li>
<b>POISSON_CDF_VALUES</b> returns some values of the Poisson CDF.
</li>
<li>
<b>POLYLOGARITHM_VALUES</b> returns some values of the polylogarithm.
</li>
<li>
<b>PRANDTL_VALUES</b> returns some values of the Prandtl number.
</li>
<li>
<b>PRIME_VALUES</b> returns values of the prime function.
</li>
<li>
<b>PSAT_VALUES</b> returns some values of the saturation pressure.
</li>
<li>
<b>PSI_VALUES</b> returns some values of the Psi or Digamma function.
</li>
<li>
<b>R8_FACTORIAL_VALUES</b> returns values of the real factorial function.
</li>
<li>
<b>R8_FACTORIAL_LOG_VALUES</b> returns values of log(n!).
</li>
<li>
<b>RAYLEIGH_CDF_VALUES</b> returns some values of the Rayleigh CDF.
</li>
<li>
<b>SECVIR_VALUES</b> returns some values of the second virial coefficient.
</li>
<li>
<b>SHI_VALUES</b> returns some values of the hyperbolic sine integral function.
</li>
<li>
<b>SI_VALUES</b> returns some values of the sine integral function.
</li>
<li>
<b>SIGMA_VALUES</b> returns some values of the Sigma function.
</li>
<li>
<b>SIN_VALUES</b> returns some values of the sine function.
</li>
<li>
<b>SIN_DEGREE_VALUES:</b> the sine function with argument in degrees.
</li>
<li>
<b>SIN_POWER_INT_VALUES</b> returns some values of the sine power integral.
</li>
<li>
<b>SINH_VALUES</b> returns some values of the hyperbolic sine function.
</li>
<li>
<b>SIX_J_VALUES</b> returns some values of the Wigner 6J function.
</li>
<li>
<b>SOUND_VALUES</b> returns some values of the speed of sound.
</li>
<li>
<b>SPHERE_UNIT_AREA_VALUES</b> returns some areas of the unit sphere in ND.
</li>
<li>
<b>SPHERE_UNIT_VOLUME_VALUES</b> returns some volumes of the unit sphere in ND.
</li>
<li>
<b>SPHERICAL_HARMONIC_VALUES</b> returns values of spherical harmonic functions.
</li>
<li>
<b>SQRT_VALUES</b> returns some values of the square root function.
</li>
<li>
<b>STIRLING1_VALUES</b> returns some values of the Stirling numbers, kind 1.
</li>
<li>
<b>STIRLING2_VALUES</b> returns some values of the Stirling numbers, kind 2.
</li>
<li>
<b>STROMGEN_VALUES</b> returns some values of the Stromgen function.
</li>
<li>
<b>STRUVE_H0_VALUES</b> returns some values of the Struve H0 function.
</li>
<li>
<b>STRUVE_H1_VALUES</b> returns some values of the Struve H1 function.
</li>
<li>
<b>STRUVE_L0_VALUES</b> returns some values of the Struve L0 function.
</li>
<li>
<b>STRUVE_L1_VALUES</b> returns some values of the Struve L1 function.
</li>
<li>
<b>STUDENT_CDF_VALUES</b> returns some values of the Student CDF.
</li>
<li>
<b>STUDENT_NONCENTRAL_CDF_VALUES</b> returns values of the noncentral Student CDF.
</li>
<li>
<b>SUBFACTORIAL_VALUES</b> returns values of the subfactorial function.
</li>
<li>
<b>SURTEN_VALUES</b> returns some values of the surface tension.
</li>
<li>
<b>SYNCH1_VALUES</b> returns some values of the synchrotron radiation function.
</li>
<li>
<b>SYNCH2_VALUES</b> returns some values of the synchrotron radiation function.
</li>
<li>
<b>TAN_VALUES</b> returns some values of the tangent function.
</li>
<li>
<b>TANH_VALUES</b> returns some values of the hyperbolic tangent function.
</li>
<li>
<b>TAU_VALUES</b> returns some values of the Tau function.
</li>
<li>
<b>THERCON_VALUES</b> returns some values of the thermal conductivity.
</li>
<li>
<b>THREE_J_VALUES</b> returns some values of the Wigner 3J function.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRAN02_VALUES</b> returns some values of the order 2 transportation function.
</li>
<li>
<b>TRAN03_VALUES</b> returns some values of the order 3 transportation function.
</li>
<li>
<b>TRAN04_VALUES</b> returns some values of the order 4 transportation function.
</li>
<li>
<b>TRAN05_VALUES</b> returns some values of the order 5 transportation function.
</li>
<li>
<b>TRAN06_VALUES</b> returns some values of the order 6 transportation function.