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- W1979203929 abstract "We investigate the hyperbolic equation with two singular lines ∂2∂ξ + 2α+1ξ∂∂ ξu (ξ, ν)=∂2∂ ν2 + 2α1ν∂∂ νu(ξ,ν), 0<ξ,ν<∞, for |α|<12, under the assumption that a certain asymptotic behavior of u and its partial derivatives is prescribed for (ξ, ν) tending to the coordinate axes or to infinity. Intending to establish integral formulas for products of Bessel functions which a priori solve such a problem, we are looking for an unusual representation of the solution u(x, y), 0<x,y<∞, in terms of “initial data” outside the interval |x − y| ⩽ ξ ⩽ x+y. This will be achieved essentially by choosing a novel geometric configuration of six subregions of the domain, to which Green's theorem will be applied. Moreover, we employ detailed knowledge about the corresponding Riemann function and a further auxiliary function associated to it. In this way, various product formulas are obtained, one of which is equivalent to a recent result of Askey et al. (1986), who evaluated an integral over a triple product of Bessel functions of the first and second kind. We also give a new proof of a product formula for modified Bessel functions due to Durand." @default.
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- W1979203929 date "1994-06-01" @default.
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- W1979203929 title "Integral formulas associated with products of Bessel functions: a new partial differential equation approach" @default.
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- W1979203929 doi "https://doi.org/10.1016/0377-0427(92)00011-w" @default.
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