NorlundB
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- The Nørlund polynomials satisfy the generating function relation
.
- The Bernoulli numbers are given by
. Generalized Bernoulli numbers are given by higher integer values of a.
- The generalized Bernoulli polynomials satisfy the generating function relation
.
.
- The Bernoulli polynomials are given by
.
- NorlundB can be evaluated to arbitrary numerical precision.
- NorlundB automatically threads over lists.
Examples
open all close allScope (3)
Applications (6)
Higher-order generalized Bernoulli numbers:
Compare with their integral definition:
Generate the Nørlund numbers from their exponential generating function:
Define a function for computing the Gregory coefficients (also known as the Bernoulli numbers of the second kind):
Compute the first 10 Gregory coefficients:
These coefficients appear in the series expansion of the function :
Compare with their integral definition:
Express Stirling numbers of both kinds in terms of Nørlund polynomials:
Expand a ratio of Gamma functions at infinity using the Tricomi–Erdélyi formula:
Compare with the direct expansion:
An explicit expression for the k-order derivative of
:
Compare with the result of D:
See Also
Related Guides
Related Links
History
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
BibTeX
@misc{reference.wolfram_2025_norlundb, author="Wolfram Research", title="{NorlundB}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/NorlundB.html}", note=[Accessed: 07-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_norlundb, organization={Wolfram Research}, title={NorlundB}, year={2007}, url={https://reference.wolfram.com/language/ref/NorlundB.html}, note=[Accessed: 07-August-2025]}