tailieunhanh - Handbook of mathematics for engineers and scienteists part 165

Handbook of mathematics for engineers and scienteists part 165. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | 1116 Finite Sums and Infinite Series 2. in si p Cm 2 m 2 k 1 3. n-1 -1 k cosm k 0 nk n 4. n-1 -1 k cos k 0 nk n 1 1 - - 1 m m 0 1 . n- 1. n 2 1 . Functional Sums . Sums involving hyperbolic functions. 1. n-1 E k 0 sinh kx a sinh n - 1 - x a 2 sinh nx 2 sinh x 2 2. n-1 1 cosh kx a cosh i 2 x a k 0 sinh nx 2 sinh x 2 3. n-1 1 V -1 k sinh kx a 1 0 2 cosh x 2 sinh fa - 2 j -1 sinh f 2 2 1 x a 4. n-1 1 V -1 k cosh kx a 0 2 cosh x 2 cosh f a - x j -1 n cosh f 2 x a 5. 6. 7. n-1 1 k sinh kx a nfr2 2 n sinh n - 1 x a - n -1 sinh nx a - sinh a I. n-1 1 k cosh kx a nfr2 2 I n cosh n -1 x a - n -1 cosh nx a -cosh a I. n-1 1 - 1 kk sinh kx a fr2 2 2 -1 -1 n sinh n - 1 x a -1 n-1 n - 1 sinh nx a -sinh a I. 8. 9. 10. n-1 1 - 1 kk cosh kx a h2 2 -1 ra-1ncosh n - 1 x a - 1 -1 n - 1 cosh nx a - cosh a I. c sinh kx a 2n cosh 2 sinh f a . k 0 y2 c cosh kx a 2n cosh 2 cosh f a . k 0 . Finite Sums 1117 11. En 1 k . a sinh x - an sinh nx an 1 sinh n - 1 x ak sinh kx -------------1 .------2----2---- 1 - 2a cosh x a2 k 1 12. 13. En 1 k 1 - a cosh x - an cosh nx an 1 cosh n - a cosh kx --------------- -------------2-------- 1 - 2a cosh x a2 k 0 n1 x 1 x tanh r- coth x--coth . 2k 2k 2n 2n k 1 1 x 14. 2 2k tanh 2kx 2n coth 2nx - coth x. k 0 . Sums involving trigonometric functions. 1. 2. 3. 4. n 2 sin 2kx sin n 1 x sin nx cosec x. k 1 n cos 2kx sin n 1 x cos nx cosec x. k 0 n 2 sin 2k - 1 x sin2 nx cosec x. k 1 n 2 cos 2k - 1 x sin nx cos nx cosec x. k 1 5. n-1 1 2 sin kx a sin i 2 x a j sin cosec . k 0 6. n-1 1 2 cos kx a cos I ----x a sin cosec . k 0 2 2 2 7. 8. 9. 10. 2n-1 2n 1 x yy- 1 k cos kx a sin I -------x a sin nx sec . k 0 2 2 y - 1 k 1 sin 2k - 1 x - 1 n 1 y 2nx . 2 cos x k 1 - 1 k cos 2kx 1 -1 cos 2n 1 x k 1 En . 2 n cos n 1 x sin nx sin x - 2 sin x k 1 2 cos x 1118 Finite Sums and Infinite Series 11. yc n cos n 1 x sin nx 2 2 sin x k i 12. n-1 52 k sin 2kx k i sin 2nx n cos 2n - 1 x - 4 sin2 x 2 sin x 1O x n sin 2n - 1 x 1 -cos 2nx k cos 2kx .