Gamma function

gamma functions

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

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

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/

Author(s)

Robin K. S. Hankin

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