id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4237	Reynolds, Robert; Stauffer, Allan 	A Quadruple Integral Involving the Legendre Function Pn(x) of the First Kind: Derivation and Evaluation	2022	7	.pdf	application/pdf	2074	107	77	∫ 1 0 ∫ 1 0 ∫ 1 0 ∫ 1 0 xm−1Pv(x) log −m ( 1 t ) log 1 2 (m−v−1) ( 1 y ) log m+v 2 ( 1 z ) logk ax √ log ( 1 y )√ log ( 1 z ) log ( 1 t ) The Hurwitz-Lerch zeta Function The Hurwitz-Lerch zeta function (25.14) in [1] has a series representation given by Φ(z, s, v) = ∞∑ n=0 (v + n)−szn (4) where |z|< 1, v ̸= 0,−1, .. and is continued analytically by its integral representation given by Φ(z, s, v) = 1 Γ(s) ∫ ∞ 0 ts−1e−vt 1− ze−t dt = 1 Γ(s) ∫ ∞ 0 ts−1e−(v−1)t et − z dt (5) where Re(v) > 0, and either |z|≤ 1, z ̸= 1, Re(s) > 0, or z = 1, Re(s) > 1. 4.2.	cache/ejpam-4237.pdf	txt/ejpam-4237.txt