id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4259	Reynolds, Robert; Stauffer, Allan 	Triple Integral involving the Bessel-Integral Function Jiv(z): Derivation and Evaluation	2022	8	.pdf	application/pdf	2469	127	77	On some expansions for bessel integral functions. Math, 15 (3) (2022), 916-923 918 = − 1 2πi ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 ∫ C 1 v2Γ(v) 2−vaww−k−1(m+ w)xm+w−1(αx)ve−by2−cz2 y−m+v−w+1z−m−v−w+1 1F2 ( v 2 ; v 2 + 1, v + 1;−1 4 x2α2 ) dwdxdydz = − 1 2πi ∫ C ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 1 v2Γ(v) 2−vaww−k−1(m+ w)xm+w−1(αx)ve−by2−cz2 y−m+v−w+1z−m−v−w+1 1F2 ( v 2 ; v 2 + 1, v + 1;−1 4 x2α2 ) dxdydzdw = 1 2πi ∫ C πaww−k−12m+w−3α−m−wb 1 2 (m−v+w−2)c 1 2 (m+v+w−2) csc ( 1 2 π(m+ v + w) ) dw (5) from equation (4) in [2], equation (3.37.4.1) in [1] and equation (3.326.2) in [4] where 0 < Re(w + m) < 2, Re(m) < Re(v) < 2, α ∈ R+ and using the reflection formula (8.334.3) in [4] for the Gamma function.	cache/ejpam-4259.pdf	txt/ejpam-4259.txt