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zeta

  

the Riemann Zeta function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

zeta(z)

zeta(n,z)

Parameters

z

-

algebraic expression

n

-

(optional) algebraic expression, understood to be a non-negative integer

Description

• 

The zeta function is defined for Re(z)>1 by

zetaz=i=11iz

and is extended to the rest of the complex plane (except for the point z=1) by analytic continuation. The point z=1 is a simple pole.

• 

The call zeta(n, z) gives the nth derivative of the zeta function,

zetan,z=ⅆnⅆznzetaz

• 

zeta(z) will evaluate by default only when the result is an exact value, or when the input z is a floating point number.  When z is a symbolic expression, it will remain in function form so that it can be manipulated symbolically by itself or as part of a larger expression.  

• 

If z is an array or matrix, the result is an element-wise mapping over z.

Examples

withMTM:

zeta1,12

ζ12γ2+ln8π2+π4

(1)

See Also

MTM

Zeta