By I.S. Gradshteyn, I.M. Ryzhik
Desk of Integrals, sequence and items
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Additional info for Table of Integrals, Series, and Products
Sample text
Q(q^\)(2^-^-q) η Λ! · A: = (n - F - 1)! 131 2 i = C + 1. 1) of reciprocals l n of „ " + J 7 - 2 ( natural numbers , Η - 1 ) Λ + * - 1 ) · where ι ^lfc = 4 " ^ * ( ! - * ) ( 2 - * ) ( 3 - x ) . . ( f e - l - x ) r f x . ι a ' &α· Α =1 2 2 _ 1Q ' ~ 9 3 12 A * = W' J O (59), A D (1876) (Ο. 141 [p + (k—\)q](p-\-kq) GIΙΠ (64 )a p{p + nq) ' η 2. Σ [p±(k-\) q] (p + kq) [p +(k-f-\) η (2p + nq + q) 2p (p + q) (p + nq)[p+(n q] + i) q] GI M 1 - (65)a f Λ=1 ( P - F *<7) [ρ-Τ-(Λ + 1 ) Λ . . [ Ρ + ( Λ + / ) Λ 4.
4. 316 1. n (cos χ 4- i sin x) = cos nx 4- i sin nx. n 2. (ch χ 4- sh x) = sh nx + ch rcy sh | = ± j / l(chz-l) [/? i s an i n t e g e r ] . 317 1. sin I = ± ] / | d - cosa:). 2. 317 2 . 317 3 . are taken so a s to agree with the s i g n s of the left hand members. T h e sign of the left hand members d e p e n d s in turn on the value of x. 320 n-t 1. 2. 2 sin*"* = - ^ { 2 2 ( - i r ' ' 2 ( ; ) c o s 2 ( n - A) 2; + ( ; ) } . n h {2 S ' " z = < ^ i L ( - i r f c 2 2 ( ; ) c h 2 ( n - Ä ) * KR 56 (10,2) 2 + ( ; ) } .
3 Î 2 P o w e r s e r i e s may be integrated circle of c o n v e r g e n c e ; that i s , X oo I k=0 and differentiated termwise i n s i d e the fc=0 oo oo T h e r a d i u s of c o n v e r g e n c e of a s e r i e s that i s o b t a i n e d from termwise integration or differentiation of another power s e r i e s c o i n c i d e s with the r a d i u s of c o n v e r g e n c e of the original s e r i e s . O p e r a t i o n s on power s e r i e s 0 . 3 1 3 Division of power s e r i e s . CD • = — Σ Σ fe=0 k ν * .