gsl (version 2.1-8)

Gamma: gamma functions

Description

Gamma functions as per the Gnu Scientific Library reference manual section 7.19. These functions are declared in header file gsl_sf_gamma.h

Usage

gsl_sf_gamma(x,give=FALSE,strict=TRUE)
lngamma(x,give=FALSE,strict=TRUE)
lngamma_sgn(x,give=FALSE,strict=TRUE)
gammastar(x,give=FALSE,strict=TRUE)
gammainv(x,give=FALSE,strict=TRUE)
lngamma_complex(zr, zi=NULL, r.and.i=TRUE, give=FALSE, strict=TRUE)
taylorcoeff(n,x,give=FALSE,strict=TRUE)
fact(n,give=FALSE,strict=TRUE)
doublefact(n,give=FALSE,strict=TRUE)
lnfact(n,give=FALSE,strict=TRUE)
lndoublefact(n,give=FALSE,strict=TRUE)
gsl_sf_choose(n,m,give=FALSE,strict=TRUE)
lnchoose(n,m,give=FALSE,strict=TRUE)
poch(a,x,give=FALSE,strict=TRUE)
lnpoch(a,x,give=FALSE,strict=TRUE)
lnpoch_sgn(a,x,give=FALSE,strict=TRUE)
pochrel(a,x,give=FALSE,strict=TRUE)
gamma_inc_Q(a,x,give=FALSE,strict=TRUE)
gamma_inc_P(a,x,give=FALSE,strict=TRUE)
gamma_inc(a,x,give=FALSE,strict=TRUE)
gsl_sf_beta(a,b,give=FALSE,strict=TRUE)
lnbeta(a,b,give=FALSE,strict=TRUE)
beta_inc(a,b,x,give=FALSE,strict=TRUE)

Arguments

x,a,b

input: real values

m,n

input: integer value

zr

In gamma_complex(), the real part of the argument

zi

In gamma_complex(), the imaginary part of the argument. If missing (ie takes the default value of NULL), interpret zr as complex, even if real

r.and.i

In gamma_complex(), Boolean variable with default value of TRUE meaning to return a complex variable as per the details section below; and FALSE meaning to return the values as advertised in the GSL manual

give

Boolean with TRUE meaning to return a list of three items: the value, an estimate of the error, and a status number

strict

Boolean, with TRUE meaning to return NaN if status is an error

Author

Robin K. S. Hankin

Details

All functions as documented in the GSL reference manual section 7.19.

Note that gamma_inc_P() gives the area of the left tail of the gamma distribution so, for example, gamma_inc_P(1.8, 5) = pgamma(5, 1.8) to numerical accuracy.

References

https://www.gnu.org/software/gsl/

Examples

gsl_sf_gamma(3)

lngamma_complex(1+seq(from=0,to=5,by=0.1)*1i)  #table 6.7, p 277 (LH col)
                                               #note 2pi phase diff


jj <- expand.grid(1:10,2:5)
x <- taylorcoeff(jj$Var1,jj$Var2)
dim(x) <- c(10,4)
x    #table 23.5, p818


jj <- expand.grid(36:50,9:13)
x <- gsl_sf_choose(jj$Var1,jj$Var2)
dim(x) <- c(15,5)
x     #table 24.1, p829  (bottom bit)

gamma_inc(1.2,1.3)
beta(1.2, 1.3)
lnbeta(1.2,1.55)
beta_inc(1.2,1.4,1.6)

gamma_inc_P(1.8, 5) - pgamma(5, 1.8)  # should be small