NorlundB
NorlundB[n,a]
gives Nørlund polynomials of degree n in a.
NorlundB[n,a,x]
gives generalized Bernoulli polynomials .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- The Nørlund polynomials satisfy the generating function relation
.
- The generalized Bernoulli polynomials satisfy the generating function relation
.
- The Bernoulli numbers are given by
. Generalized Bernoulli numbers are given by higher integer values of a.
- NorlundB can be evaluated to arbitrary numerical precision.
- NorlundB automatically threads over lists.
Examples
open allclose allScope (3)
Applications (4)
Higher-order generalized Bernoulli numbers:
Compare with their integral definition:
Expand ratio of Gamma functions at infinity:
Wolfram Research (2007), NorlundB, Wolfram Language function, https://reference.wolfram.com/language/ref/NorlundB.html.
Text
Wolfram Research (2007), NorlundB, Wolfram Language function, https://reference.wolfram.com/language/ref/NorlundB.html.
CMS
Wolfram Language. 2007. "NorlundB." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NorlundB.html.
APA
Wolfram Language. (2007). NorlundB. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NorlundB.html