
zeta - Riemann zeta function

Calling sequence:

zeta(x)

Parameter:

x  --   expression

Overloading:

1

Summary:

The zeta function is defined as

    zeta(x) = sum( i^(-x), i=0..infinity )

If x is a negative, even integer, then

    zeta(x) = 0,

if x is a negative, odd integer, then

    zeta(x) = - bernoulli(x) / (1-x),

if x is zero, then

     zeta(x) = -1/2,

if x is a positive, even integer, then

     zeta(x) = ((2*PI)^x)/2 * abs(bernoulli(x)/fact(x)).

zeta returns the function call with evaluated arguments, if the argument
cannot be evaluated to a number. zeta is a kernel function.

>>  zeta(-23);

      236364091/65520

>>  zeta(3-I); float(%);

      zeta(3 - I)

      1.107214408 + 0.1482908671 I

See also:  bernoulli

