id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-2293	Bin-Saad, Maged Gumman	Fractional generalization of Rodrigues-type Formulas for Certain Class of Special Functions	2015	12	.pdf	application/pdf	4032	218	85	Then DF (β ,γ) ν (a, b, k; x) =(ν+ 1)F (β ,γ) ν+1 (a, b, k; x) + � akxk − β x � F (β ,γ) ν (a, b, k; x), (43) (ν+ 1)F (β ,γ) ν+1 (a, b, k; x) = � β + bγ � F (β−1,γ) ν (a, b, k; x)− akF (β+k−1,γ) ν (a, b, k; x), (44) νF (β ,γ) ν (a, b, k; x) = � β + bγ � F (β−1,γ) Then xβ e−axk ∞ ∑ s=0 � ν s � Γ(ν− s+ 1)F (β ,γ) ν−s (a, b, k; x) � Ds f (x) � =In−v � xβ+bγe−axk � D+ β + bγ− akxk x �n f (x) � , (51) xβ e−axk ∞ ∑ s=0 � ν s � Γ(ν− s+ 1)F (β ,γ) ν−s (a, b, k; x) � Ds f (x) � =In−v ¦ Ω n,m β ,γ,b (x) � D− akxk−1 �m f (x) © , (52) where Ω n,m β ,γ,b (x) = n ∑ m=0 � n n−m �� β + bγ n−m � (n−m)!eaxk xβ+bγ+m−n, and xβ e−axk ∞ ∑ s=0 � ν s � Γ(ν− s+ 1)F (β ,γ) ν−s (a, b, k; x) � Ds f (x) � =In−v ( xβ+bγ−ne−axk n−1 ∏ j=0 � x D+ β + bγ− j − akxk � f (x) ) .	cache/ejpam-2293.pdf	txt/ejpam-2293.txt