Zeta function

Zeta functions

Zeta functions as per the Gnu Scientific Library 7.31 and AMS-55, section 23.2. These functions are declared in header file gsl_sf_zeta.h

zeta_int(n, give=FALSE, strict=TRUE)
zeta(s, give=FALSE, strict=TRUE)
zetam1_int(n, give=FALSE, strict=TRUE)
zetam1(s, give=FALSE, strict=TRUE)
hzeta(s, q, give=FALSE, strict=TRUE)
eta_int(n, give=FALSE, strict=TRUE)
eta(s, give=FALSE, strict=TRUE)

Arguments

• n: input: integer values

• s,q: input: real values

• 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.

References

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

Author(s)

Robin K. S. Hankin

Examples

n <- 1:10
cbind(n,zeta(n),eta(n))   #table 23.3, p 811

zeta_int(1:5)
zeta(c(pi,pi*2))
zetam1_int(1:5)
zetam1(c(pi,pi*2))
hzeta(1.1,1.2)
eta_int(1:5)
eta(c(pi,pi*2))