id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4282	Reynolds, Robert; Stauffer, Allan 	A Triple Integral Containing the Lommel Function su,v(z): Derivation and Evaluation	2022	7	.pdf	application/pdf	2250	117	77	Math, 15 (3) (2022), 992-998 994 1F2 ( 1; u 2 − v 2 + 3 2 , u 2 + v 2 + 3 2 ;−1 4 x2α2 ) dxdydz = 1 2πi ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 ∫ C αaww−k−1e−b(y2+z2)xm+w(αx)uy−m−v−w+1z−m+v−w+1 u2 + 2u− v2 + 1 1F2 ( 1; u 2 − v 2 + 3 2 , u 2 + v 2 + 3 2 ;−1 4 x2α2 ) dwdxdydz = 1 2πi ∫ C ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 αaww−k−1e−b(y2+z2)xm+w(αx)uy−m−v−w+1z−m+v−w+1 u2 + 2u− v2 + 1 1F2 ( 1; u 2 − v 2 + 3 2 , u 2 + v 2 + 3 2 ;−1 4 x2α2 ) dxdydzdw = 1 2πi ∫ C πaww−k−1bm+w−2 ( −2m+u+w−4 ) α−m−w Γ ( 1 2 (u− v + 1) ) Using a generalization of Cauchy’s integral formula we form the triple integral by replacing y by log ( ax yz ) and multiplying by αxme−b(y2+z2)y−m−v+1z−m+v+1(αx)u 1F2 ( 1; u2 − v 2 + 3 2 , u 2 + v 2 + 3 2 ;− 1 4x 2α2 ) u2 + 2u− v2 + 1 then taking the definite integral with respect to x ∈ [0,∞), y ∈	cache/ejpam-4282.pdf	txt/ejpam-4282.txt