NevilleThetaD

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

For fixed z

For fixed m

General characteristics

Domain and analyticity

(Subscript[ϑ, d])(z|m) is an analytical meromorphic function of z and m which is defined over (ℂ^2).

Symmetries and periodicities

Parity

(Subscript[ϑ, d])(z|m) is an even function with respect to z.

Mirror symmetry

Periodicity

(Subscript[ϑ, d])(z|m) is a periodic function with respect to z with period 2 K(m) .

Branch points

Branch points locations: complicated

Branch cuts

Branch cut locations: complicated

Series representations

Generalized power series

Product representations

Differential equations

Partial differential equations

Transformations

Transformations and argument simplifications

Argument involving basic arithmetic operations

Differentiation

Low-order differentiation

With respect to z

Symbolic differentiation

With respect to z

Fractional integro-differentiation

With respect to z

Integration

Indefinite integration

Involving only one direct function

Representations through equivalent functions

With related functions

Involving Jacobi and other Neville functions

Involving theta functions

History

– K. Weierstrass (1894)
– E. N. Neville (1944)

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