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

John Dougall

doi:10.1017/S0013091500035380

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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.

References

page 33 note * Math. Annalen, Band xvi. (1880).

page 34 note * Cf. a paper, “The Determination of Green's Fonotion by means of Cylindrical or Spherioal Harmonics.” Proc. Edin. Math. Soc, Vol. XVIII., 1899–1900.Google Scholar

page 47 note * Handbuch der Kugelfunctionen, Zwtittr Band, s. 368.

Crossref Citations

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

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