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Gegenbauer addition theorem

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1: 10.44 Sums
Graf’s and Gegenbauer’s Addition Theorems
2: 10.23 Sums
Graf’s and Gegenbauer’s Addition Theorems
See accompanying text
Figure 10.23.1: Graf’s and Gegenbauer’s addition theorems. Magnify
3: Bibliography C
  • B. C. Carlson (1971) New proof of the addition theorem for Gegenbauer polynomials. SIAM J. Math. Anal. 2, pp. 347–351.
  • H. S. Cohl (2013a) 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.
  • 4: 18.18 Sums
    §18.18(ii) Addition Theorems
    Ultraspherical
    Legendre
    Laguerre
    Hermite
    5: 10.60 Sums
    §10.60(i) Addition Theorems
    6: 14.28 Sums
    §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
  • Additions

    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. …
  • Chapters 14 Legendre and Related Functions, 15 Hypergeometric Function

    The Gegenbauer function C α ( λ ) ( z ) , was labeled inadvertently as the ultraspherical (Gegenbauer) polynomial C n ( λ ) ( z ) . 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).

  • Subsections 9.6(iii), 22.19(i)

    Minor additions have been made.