RiemannSiegelZ

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

Values at fixed points

General characteristics

Domain and analyticity

Z(z) is an analytical function of z which is defined over the whole complex z-plane.

Symmetries and periodicities

Parity

Z(z) is an even function.

Mirror symmetry

Periodicity

No periodicity

Poles and essential singularities

The function Z(z) does not have poles and essential singularities.

Branch points

Branch cuts

Series representations

Generalized power series

Expansions at z==(i/2)

Expansions at z==-(i/2)

Expansions at z==(Subscript[z, 0])/; (Subscript[z, 0])≠-n

Expansions at z==(i/2)+2i k

Expansions at z==-(i/2)-2i k

Asymptotic series expansions

Identities

Recurrence identities

Differentiation

Low-order differentiation

Symbolic differentiation

Integration

Definite integration

Representations through equivalent functions

With related functions

History

– B. Riemann (1859)
– C. L. Siegel (1932)

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