gamma

Contents: Description, Arguments, Usage, Examples, Sub-Functions, Related Functions, Source Supported Under Version: >1.00 Current .dvrc Version: 1.29 Description Gamma function (extended factorial). Arguments and Return Values Arguments: One numeric array Return Value: An array of the same organization as the input, containing the gamma function evaluated at each element of the input. gamma(n) = fact(n-1) = (n-1)! for positive integers and half-integers gamma(x) = Γ(x) = integral from zero to infinity of t^(x-1)*exp(-t) with respect to t Γ(x+1) = x*Γ(x) The gamma function is undefined (infinite) for negative integers and zero. This function returns zero for those values. This function uses a numerical approximation from W. J. Cody and L. Stoltz, which is accurate to the precision of the input. Return format is double for double input; float otherwise. If no arguments are input, gamma() prints its description, as shown below. Usage Syntax: gamma(x) 'x' - any numeric array If x is double format, gamma(x) for x > 171 evaluates to infinity, since the calculated value is greater than the maximum double value. If x is not double format, gamma(x) for x > 35 evaluates to infinity, being above the maximum float value. Examples dv> gamma() Gamma function - extended factorial gamma(x) = fact(x-1) gamma(x) = integral from 0 to Inf of t^(x-1)*exp(-t) dt gamma(x+1) = x*gamma(x) Accurate within precision of input Works for arrays This function uses an algorithm from W. J. Cody and L. Stoltz See http://www.netlib.org/specfun/gamma S.Marshall 02-22-2008 0 dv> x 10x1x1 array of float, bsq format [40 bytes] 0.500000 1.00000 1.50000 2.00000 2.50000 3.00000 3.50000 4.00000 4.50000 5.00000 dv> gamma(x) 10x1x1 array of float, bsq format [40 bytes] 1.77245 1.00000 0.886227 1.00000 1.32934 2.00000 3.32335 6.00000 11.6317 24.0000 dv> gamma(0) Division by zero, 1 times Negative integers and zero are not allowed! Output set to zero at those values. 0.00000 dv> gamma(35//36) 2x1x1 array of float, bsq format [8 bytes] 2.95232e+38 inf

DavinciWiki Mini-Nav Bar Contents Functions Function Categories Common Procedures Glossary Download Davinci Change Log News Mailing List Contact Developers davinci-dev [AT] mars.asu.edu All other topics See navigation on the left Major Sub-Functions atod create dim format isint isnum Related Functions fact math.dvrc gamma() Recent Library Changes Change Log Created On: 02-22-2008 Modified On: 02-26-2008