Gegenbauer addition theorem

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1: 10.44 Sums

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Graf’s and Gegenbauer’s Addition Theorems

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2: 10.23 Sums

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Graf’s and Gegenbauer’s Addition Theorems

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Figure 10.23.1: Graf’s and Gegenbauer’s addition theorems. Magnify

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3: Bibliography C

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New proof of the addition theorem for Gegenbauer polynomials. SIAM J. Math. Anal. 2, pp. 347–351.

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External Links:

ISSN 1095-7154, Document, MathReview (Mary L. Boas), ZentralBlatt

Referenced by:

§18.18(ii).

Encodings:

BibTeX

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Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems. SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 042, 26.

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External Links:

ISSN 1815-0659, Document, MathReview (Heinrich Begehr), ZentralBlatt

Referenced by:

§14.28(ii), §14.28(ii).

Encodings:

BibTeX

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4: 18.18 Sums

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§18.18(ii) Addition Theorems

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Ultraspherical

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Legendre

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Laguerre

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Hermite

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5: 10.60 Sums

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§10.60(i) Addition Theorems

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6: 14.28 Sums

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§14.28(i) Addition Theorem

… ►For generalizations in terms of Gegenbauer and Jacobi polynomials, see Theorem 2. 1 in Cohl (2013b) and Theorem 1 in Cohl (2013a) respectively. …

7: Errata

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Equations: (15.6.2_5), (17.2.6_1), (17.2.6_2), a new inequality, with clarifications, was added to (7.8.7).

… ►This release increments the minor version number and contains considerable additions of new material and clarifications. These additions were facilitated by an extension of the scheme for reference numbers; with “_” introducing intermediate numbers. … ►

The Gegenbauer function $C_{\alpha }^{(\lambda )}\left(z\right)$, was labeled inadvertently as the ultraspherical (Gegenbauer) polynomial $C_n^{(\lambda )}\left(z\right)$. In order to resolve this inconsistency, this function now links correctly to its definition. This change affects Gegenbauer functions which appear in §§14.3(iv), 15.9(iii).

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Minor additions have been made.

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