Handbook of mathematics for engineers and scienteists part 166. 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. | . Infinité Series 1123 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. œ -1 k E k2 sin kx k 1 1 n 1 2n 2n 1 B x n 2 2n 1 2ra 1 2n where -n x n for n 0 1 . the Bn x are Bernoulli polynomials. œ 1 sin kx exp cos x sin sin x k k 1 x is any number. -1 k k k 1 sin kx -exp -cos x sin sin x œ 1 - sin kx sin I sin sinh I cos 2k V 2 2 k 0 œ -1 k x î x v - sin kx - sin I cos sinh I sin 2k 2 2 k 0 œ k a sin kx exp k cos x sin k sin x k k 0 œ ak sin kx k 0 œ kak sin kx k 1 x is any number. x is any number. x is any number. a 1 x is any number. a sin x 1 - 2a cos x a2 a 1 x is any number. a 1 - a2 sin x -------------5-3- a 1 x is any number. 1 - 2a cos x a2 2 œ1 E sin kx a k k 1 2 n -x cos a-lnf2sin 2 j sina 0 x 2n. k 1 sin kx a 2 x cos a ln f 2 cos 2 j sin a œ sin 2k - 1 x n 2k - 1 4 k 1 œ -1 k-1 k 1 sin 2k - 1 x 2k - 1 -n x n. 0 x n. lntanfx i 2 2 4 n n - 2 x 2 f a2k-1 s 2 - 1 x arctan 2 0 x 2n a 1. 2k -1 2 1 - a2 k 1 œ -1 k-1 a2k-1 k 1 sin 2k - 1 x 2k - 1 1 1 2a sin x a2 4 1 - 2a sin x a2 0 x n a 1. .k sin k 1 x ZÎ k k 1 1 sin x - 2 x 1 cos x - sin x ln x 2 cos . 2 1124 Finite Sums and Infinite Series 31. 2k 1 r o . i a 1 a2 sinx a sin 2k 1 x yy a 1 x is any number. 1 a2 2 - 4a2 cos2 x k 0 v 7 32. X z .k 2k 1 . . a 1 - a2 sinx -1 a sin 2k 1 x yy a 1 x is any number. 1 a2 2 - 4a2 sin2 x k 0 v 7 33. y sin 2 fc l x sin 2x - n - 2x sin2 x - sin x cos x ln 4 sin2 x 0 x n. k k 1 k 1 34. k sin 2k 1 x _ 4nx if -1n x n 2k 1 2 4n n - x if n x n. . Trigonometric series in one variable involving cosine. 1. œ i v 1 cos kx -lni 2sin 2 0 x 2n. k l 7 2. œ -1 k-1 x 2-j k cos kx In i 2 cos 2 F -n x n. k 1 7 3. œ a 1 z. . . . . cos kx In -y 0 x 2n a 1. k 1 k V1 - 2a cos x a2 œ 1 4. - cos kx sin cos - ln cot2 0 x 2n. 2k 1 4 2 2 V 4 k 0 7 5. œ z i k 1 __ __ . y . 1 cos kx -1 sin x Infcot2 cos -n x n. 2k 1 4 2 4 4 2 k 0 6. œ 1 0 y -y cos kx 3x2 - 6nx 2n2 0 x 2n. k2 12 k 1 7. œ -1 k 12 2 y y cos kx 3x2 - n2 -n x n. k2 12 k 1 8. 1 cos kx X x - n sin x - 2 sin2 x ln 2 sin
