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Mathematica > Mathematics and Algorithms > Calculus > Discrete Calculus > Recurrence and Sum Functions >

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NorlundB

NorlundB[n, a]
gives Nørlund polynomials

of degree n in a.

NorlundB[n, a, x]
gives generalized Bernoulli polynomials

The Bernoulli numbers are given by . Generalized Bernoulli numbers are given by higher integer values of a.

First five Nørlund polynomials:

Generalized Bernoulli polynomials:

First five Nørlund polynomials:

Generalized Bernoulli polynomials:

NorlundB threads element-wise over lists:

Plot Nørlund polynomials:

Higher-order generalized Bernoulli numbers:

First ten Nørlund numbers:

Stirling numbers:

Expand ratio of Gamma functions at infinity: