tailieunhanh - Handbook of mathematics for engineers and scienteists part 174

Handbook of mathematics for engineers and scienteists part 174. 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. | . Tables of Fourier Cosine Transforms 1179 . Expressions with Hyperbolic Functions No. 1 Original function f x u a 0 cosh ax p Cosine transform fc u f x cos ux dx Jo n 2a cosh 2na u 2 cosh2 ax nu 2a2 sinh 2na- u 3 cosh ax v lal b cosh bx n b cos 2nab cosh 2nb u cos nab Q cosh nb u 4 1 cosh ax cos b n sinh a ibu a sinb sinh na- u 5 exp -ax2 cosh bx a 0 1 Pn b2 -u2 abu a eXP 4a W 2 6 x sinh ax n2 4a2 cosh2 2na- u 7 sinh ax 7 v a b sinh bx n sin nab 2b cos nab cosh nb u 8 tanh ax a 0 x In coth 4na u . Expressions with Logarithmic Functions No. Original function f x r Cosine transform fc u f x cos ux dx 70 1 In x if 0 x 1 to if 1 x - Si u u 2 ln x y x - iln 4u C 1 C . is the Euler constant 3 xv-1 In x 0 v 1 r v cos u-v v - n tan -lnu v 2 L 2 2 J 4 1 a x I lnl 1 a 0 1 a-x 1 2 r o- x x o cos au Si au - sin au Ci au J 5 ln 1 a2 x2 a 0 - 1 -e- au u 6 .a2 x2 . ln - a b 0 b2 x2 n -bu -au u e -e 7 e ax lnx a 0 aC 2a ln u2 a2 u arctan u a u2 a2 8 ln 1 eax a 0 a n 2u2 2u sinh na-1 u 9 ln 1 - e x a 0 - n coth no u 2u2 2u v 1180 Integral Transforms . Expressions with Trigonometric Functions No. 1 Original function f x S a 0 x r Cosine transform fc u f x cos ux dx 70 f 2 n if u a t 4 n if u a Io if u a 2 xv-1 sin ax a 0 v 1 u a -v - u a -v sign u - a n _ _ Z1 x 4r 1 - v cos 2nu 3 x sin ax 7 2 2 a b 0 x- b2 2ne. cosh bu if u a -2nA sinh ab if u a 4 sin ax 7 2 2 a b 0 x x2 b2 2A 2 1 - Aa cosh bu if u a 2A 2iA sinh ab if u a 5 e lb sin ax a b 0 2 a u a-u . a u 2 b2 a - u 2 b2 . 6 sin2 ax a 0 x 11 2 1-4 u2 7 r-sin2 ax a 0 x2 I 4 n 2a - u if u 2a I 0 if u 2a 8 sinf aY a 0 x xx n J0 2 au 9 sin a- r sin b x a b 0 V x Ja sin sin - n V u 2uJ 4u 4 J 10 sin ax2 a 0 cos 4a -sin 4a 11 exp -ax2 sin bx2 a 0 Au2 . Bu2 A2 B2 1 4 eXC A2 B2 C A2 B2 A 4a B 4b ip 2 arctan b a 12 1 COs ax a 0 x 11n t a2 1 u2 13 1 -CO ax a 0 x2 f 2 n a - u if u a 10 if u a 14 xv-1 cos ax a 0 0 v 1 4 r v cos 2 nv u - a -v u a -v 15 iO a b 0 x2 b2 2nbir- ab cosh bu if u a 2nb iB cosh ab if u a