NorlundB2

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

For fixed n

For fixed z

General characteristics

Domain and analyticity

The function (Subscript[B, n]^((z))) is defined over ℕ⊗ℂ. For fixed n, the function (Subscript[B, n]^((z))) is a polynomial in z of degree n.

Symmetries and periodicities

Parity

No parity

Mirror symmetry

Periodicity

No periodicity

Poles and essential singularities

The function (Subscript[B, n]^((z))) is polynomial and has pole of order n at z =(OverTilde[∞]).

Branch points

The function (Subscript[B, n]^((z))) does not have branch points.

Branch cuts

The function (Subscript[B, n]^((z))) does not have branch cuts.

Series representations

Generalized power series

Expansions at generic point z==(Subscript[z, 0])

Expansions at z==0

Expansions at z==∞

Other series representations

Generating functions

Identities

Functional identities

Relations between contiguous functions

Differentiation

Low-order differentiation

Pavlyk O. (2006)

Symbolic differentiation

Fractional integro-differentiation

Integration

Indefinite integration

Involving only one direct function

Summation

Finite summation

Infinite summation

Representations through more general functions

Through other functions

Representations through equivalent functions

With related functions

Copyright