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Integrals of three Bessel functions and Legendre functions. I. (English) Zbl 0586.33004
Integrals of products of three Bessel functions of the form $$ \int\sp{\infty}\sb{0}t\sp{\lambda - 1}J\sb{\mu}(at)J\sb{\nu}(bt)H\sb{\rho}\sp{(1)}(ct)dt $$ are calculated when some relations exist between the indices $\lambda$,$\mu$,$\nu$,$\rho$ : in these cases, the Appell function $F\sb 4$ factorizes into two hypergeometric functions of one variable, so that analytical continuation is possible. New results are given, mainly when a,b, and c are real and positive and $\vert a-b\vert <c<a+b$, which correspond to most physical situations.

33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
33C55Spherical harmonics
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