generating functions

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31: 14.30 Spherical and Spheroidal Harmonics

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Herglotz generating function

►The following is the Herglotz generating function …

32: 18.26 Wilson Class: Continued

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§18.26(iv) Generating Functions

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33: 26.8 Set Partitions: Stirling Numbers

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§26.8(ii) Generating Functions

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34: 26.13 Permutations: Cycle Notation

… ►See §26.8 for generating functions, recurrence relations, identities, and asymptotic approximations. …

35: Bibliography E

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Generating functions of certain continuous orthogonal systems. Proc. Roy. Soc. Edinburgh. Sect. A. 61, pp. 61–70.

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External Links:

MathReview (G. Szegő), ZentralBlatt

Referenced by:

§12.16.

Encodings:

BibTeX

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36: 15.16 Products

… ►where $A_0=1$ and $A_s$, $s=1,2,\mathrm{\dots }$, are defined by the generating function …

37: 9.17 Methods of Computation

… ►In consequence of §9.6(i), algorithms for generating Bessel functions, Hankel functions, and modified Bessel functions (§10.74) can also be applied to $\mathrm{Ai}\left(z\right)$, $\mathrm{Bi}\left(z\right)$, and their derivatives. …

38: 18.2 General Orthogonal Polynomials

… ►Polynomials $p_n(x)$ of degree $n$ ($n=0,1,2,\mathrm{\dots }$) are called Sheffer polynomials if they are generated by a generating function of the form …If $v(s)$ is the formal power series such that $v(u(t))=t$ then a property equivalent to (18.2.45) with $c_n=1$ is that … ►The generating functions (18.12.13), (18.12.15), (18.23.3), (18.23.4), (18.23.5) and (18.23.7) for Laguerre, Hermite, Krawtchouk, Meixner, Charlier and Meixner–Pollaczek polynomials, respectively, can be written in the form (18.2.45). … ►The Bernoulli polynomials $B_n\left(x\right)$ and Euler polynomials $E_n\left(x\right)$ are examples of Sheffer polynomials which are not OP’s, see the generating functions (24.2.3) and (24.2.8). …

39: Bibliography W

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Generating functions of class-numbers. Compositio Math. 1, pp. 39–68.

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External Links:

ISSN 0010-437X, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§20.7(v), §20.8.

Encodings:

BibTeX

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40: Bibliography F

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Singularity analysis of generating functions. SIAM J. Discrete Math. 3 (2), pp. 216–240.

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External Links:

ISSN 0895-4801, Document, MathReview (E. Rodney Canfield), ZentralBlatt

Referenced by:

§2.10(iv).

Encodings:

BibTeX

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