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    Clutton-Brock, M. 1987. Generalized Fejér and Lanczos Kernels. SIAM Journal on Mathematical Analysis, Vol. 18, Issue. 1, p. 259.


    van Haeringen, H. 1986. A class of sums of Gegenbauer functions: Twenty-four sums in closed form. Journal of Mathematical Physics, Vol. 27, Issue. 4, p. 938.


    Rahman, Mizan and Shah, Mihr J. 1985. Sums of products of ultraspherical functions. Journal of Mathematical Physics, Vol. 26, Issue. 4, p. 627.


    Rahman, Mizan and Shah, Mihr J. 1985. An Infinite Series with Products of Jacobi Polynomials and Jacobi Functions of the Second Kind. SIAM Journal on Mathematical Analysis, Vol. 16, Issue. 4, p. 859.


    Bressoud, D. M. 1981. Linearization and Related Formulas forq-Ultraspherical Polynomials. SIAM Journal on Mathematical Analysis, Vol. 12, Issue. 2, p. 161.


    Gasper, George 1975. Theory and Application of Special Functions.


    Bingham, N. H. 1973. Positive definite functions on spheres. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 73, Issue. 01, p. 145.


    1969. Function Theoretic Methods in Partial Differential Equations.


    McFadden, J. A. 1966. A Diagonal Expansion in Gegenbauer Polynomials for a Class of Second-Order Probability Densities. SIAM Journal on Applied Mathematics, Vol. 14, Issue. 6, p. 1433.


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  • Proceedings of the Edinburgh Mathematical Society, Volume 37
  • February 1918, pp. 33-47

A Theorem of Sonine in Bessel Functions, with two Extensions to Spherical Harmonics

Abstract

In his notable memoir on the Bessel Functions, Sonine proves the elegant result that

m > –½, provided a plane triangle can be drawn with sides a, b, c; otherwise the value of the integral is zero.

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