# relation to generalized Bernoulli polynomials

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## 1—10 of 22 matching pages

##### 1: 24.16 Generalizations

###### §24.16(ii) Character Analogs

…##### 2: 24.19 Methods of Computation

###### §24.19(i) Bernoulli and Euler Numbers and Polynomials

►Equations (24.5.3) and (24.5.4) enable ${B}_{n}$ and ${E}_{n}$ to be computed by recurrence. …For example, the tangent numbers ${T}_{n}$ can be generated by simple recurrence relations obtained from (24.15.3), then (24.15.4) is applied. … ►For algorithms for computing ${B}_{n}$, ${E}_{n}$, ${B}_{n}\left(x\right)$, and ${E}_{n}\left(x\right)$ see Spanier and Oldham (1987, pp. 37, 41, 171, and 179–180). … ►For number-theoretic applications it is important to compute ${B}_{2n}\phantom{\rule{0.949em}{0ex}}(modp)$ for $2n\le p-3$; in particular to find the*irregular pairs*$(2n,p)$ for which ${B}_{2n}\equiv 0\phantom{\rule{0.949em}{0ex}}(modp)$. …

##### 3: 25.16 Mathematical Applications

##### 4: Bibliography L

##### 5: 18.2 General Orthogonal Polynomials

###### §18.2 General Orthogonal Polynomials

… ►###### Orthogonality on General Sets

… ► … ►###### §18.2(iv) Recurrence Relations

… ► …##### 6: Bibliography B

##### 7: Bibliography C

##### 8: Bibliography Z

##### 9: Bibliography

##### 10: Software Index

This is software of narrow scope developed as a byproduct of a research project and subsequently made available at no cost to the public. The software is often meant to demonstrate new numerical methods or software engineering strategies which were the subject of a research project. When developed, the software typically contains capabilities unavailable elsewhere. While the software may be quite capable, it is typically not professionally packaged and its use may require some expertise. The software is typically provided as source code or via a web-based service, and no support is provided.

These are collections of software (e.g. libraries) or interactive systems of a somewhat broad scope. Contents may be adapted from research software or may be contributed by project participants who donate their services to the project. The software is made freely available to the public, typically in source code form. While formal support of the collection may not be provided by its developers, within active projects there is often a core group who donate time to consider bug reports and make updates to the collection.

An increasing number of published books have included digital media containing software described in the book. Often, the collection of software covers a fairly broad area. Such software is typically developed by the book author. While it is not professionally packaged, it often provides a useful tool for readers to experiment with the concepts discussed in the book. The software itself is typically not formally supported by its authors.

Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

A cross index of mathematical software in use at NIST.