Proceedings of the Edinburgh Mathematical Society

Research Article

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

Dr John Dougall

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

S0013091500035380_eqn1

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

(Received March 15 1918)

(Revised December 13 1918)