Riemann Zeta Function Minus One - GNU Scientific Library -- Reference Manual
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#### 7.32.2 Riemann Zeta Function Minus One

For large positive argument, the Riemann zeta function approaches one. In this region the fractional part is interesting, and therefore we need a function to evaluate it explicitly.

— Function: double gsl_sf_zetam1_int (int n)
— Function: int gsl_sf_zetam1_int_e (int n, gsl_sf_result * result)

> These routines compute \zeta(n) - 1 for integer n, n \ne 1.

— Function: double gsl_sf_zetam1 (double s)
— Function: int gsl_sf_zetam1_e (double s, gsl_sf_result * result)

> These routines compute \zeta(s) - 1 for arbitrary s, s \ne 1.

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