Handbook of Series for Scientists and Engineers by V. Mangulis

By V. Mangulis

Guide of sequence for Scientists and Engineers

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M ν Π " + « ) from B a . I , 104 _n«)W + b)I\l-a) 6Γ(1+6-α) U Re(«) < 1, , 1 0 , y ( ~ l ) » n W n ' ά»Κ1 + « - * ) . ^ from W h . W . 282 Γ(1 + α - & ) Γ ( 1 ) 2T(1 - 6 + 1«)Γ(1 + Ια)' 1 + β - b φ 0, - 1 . , B a . I , 104 (λλ\ K v ( * ) n W n _ I\e)IXe - a - b) I\e-a)I\e-b)' i i W n « ! , Re(c) > Re(a + 6), W h . W . 282, B a . I , 104 I\n + *)Γ(η + 6) ^Γ{η+ο)Γ{η + ά) T ' ( η ι ι \ ι = - «*(*,) csc(^) 2 r ( c _ rjc + a ) r ( g _ w _ a ) d-a-b-Y) _ r ( r f & , ) Re(# + 6 —£ —

2), Part II, Section 6 (2) V ( - ! ) " ( « " + *) n=0 = * - « ^* ; ^ from Eq. (2), Part II, Section 6 (3) 2 £ r n-l = « & » . "· where £ = 1 2 m 5 « = 1 2 3 4 15 52 203 877 4140 5 6 7 8 B r . IcsTTTj! , m ν Π " + « ) from B a . I , 104 _n«)W + b)I\l-a) 6Γ(1+6-α) U Re(«) < 1, , 1 0 , y ( ~ l ) » n W n ' ά»Κ1 + « - * ) . ^ from W h . W . 282 Γ(1 + α - & ) Γ ( 1 ) 2T(1 - 6 + 1«)Γ(1 + Ια)' 1 + β - b φ 0, - 1 . , B a . I , 104 (λλ\ K v ( * ) n W n _ I\e)IXe - a - b) I\e-a)I\e-b)' i i W n « ! , Re(c) > Re(a + 6), W h .

I, 182 F o r e x a m p l e (see also Section 2 A d of P a r t I I I ) : F,(v + 1; Λ ( " + i; 0 = 2v + 1; I\v 2w) + = \)&)-"JAz\ Γ{ν ^ ( a ; a + 1; - « ) = αζ~ γ(α, α j F j O ; + i ) ( i * ) - v v , ( * ) > ζ), 1 + α; «) = ear «*y(ur, * ) , e 2 ^ ( 1 , 1; 2; - * ) = log(l + * ) / * , Λ Ο , μ + 1; μ; ζ) = (1 + (58) - *) * . 2 + 1 ^ ( β , b; c; ζ) = (1 - *)«-·-» P,(c - α, c - 6; c; *) 2 = (1 - * ) - , * · , ( « , * - * ; = (1 - j ^ y ) (c - α, 6; c; ^ γ ) , B a . I , 105 * See W. N . Bailey, "Generalized Hypergeometric Series," Cambridge Tracts in Mathematics and Mathematical Physics, No.

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