Handbook of mathematics for engineers and scienteists part 176. 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 Inverse Mellin Transforms 1193 No. Direct transform f s Inverse transform f x 1 i ff i -- f s x- ds 2ni J a-itt 11 cos s2 a a 0 T1 cos 4a ln 2 y n 4 - 4n 12 arctan Re s -b f xb 1 -sin a ln x ln x v if 0 x 1 I 0 if 1 x . Expressions with Special Functions No. 1 2 Direct transform f s T s Re s 0 T s -1 Re s 0 1 a itt Inverse transform f x - - f s x s ds 2ni J a-ioo -x e e - 1 3 sin 2ns T s -1 Re s 1 sin x 4 sin as T s n Re s -1 a exp -x cos a sin x sin a 5 cos 2ns T s 0 Re s 1 cos x 6 cos 2ns T s -2 Re s 0 - 2 sin2 x 2 7 n cos as T s Re s 0 a exp -x cos a cos x sin a 8 0 Res 1 cos ns 2 ex erfc vx 9 r a s T b - s -a Re s b a b 0 T a b xa x 1 1-b 10 T a s T b s Re s -a -b 2x a b 2Ka-b 2Vx 11 p F s Re s 0 v 0 r v if 0 x 1 I 0 if 1 x 12 r 1 - v - s r 1 - s Re s 1 - v v 0 f 0 if 0 x 1 x - 1 V 1 if 1 x I r v 13 r s r v - s 1V 0 Re s 2 4 x v 2 Jv 2 x 14 Re v n 1 2 tTx 2Kv x 2 15 r s v T 1 2 - s r 1 v - s -v Re s 2 ni 2e x 27v x 2 16 s a - s b Re s -a -b f xb - xa n 1 J if 0 x 1 1 1 x I 0 if 1 x 17 T s s Re s 0 eJx In x 18 T s a a 0 0 if 0 x a l e x if a x 19 T s T 1 - s a Re s 0 a 0 x 1 - 1e-a x 1 1194 Integral Transforms No. 20 Direct transform f s Y s a Re s 0 a 0 Inverse transform i J if 0 x a I 0 if a x 0 1 ra i f x f s x- ds ni J cr-ioo if 0 x . cos bVa2 - ln2 x 21 J0 aVb2 s o s - s2 a 0 Re s 0 if e-a x ea if ea x 0 x e1 .1 x e e x if 0 x e1 if e1 x e if e x 22 nVa2 - ln2 x I 0 1 if n1 arccos ln x if 0 if 2v sin nv 23 Iv s Re s 0 nF x Vln2 x - 1 cos v arccos ln x nV1 - ln2 x I 0 where F x V-1 - lnx V1 -lnx 2v 24 s lv s Re s 0 f 2v sin nv 1 nvF x sin v arccos ln x 1 nv I 0 if 0 x e1 if e1 x e if e x where F x V-1 - lnx V1 -lnx 2v 25 s-V Iv s s s Re s -2 Re s 0 0 j 1 -ln2 x 1 2 if 0 x e1 if e1 x e if e x 0 x .1 .1 x 26 n 2vr v 1 2 I 0 J arccosh -ln x if 1 0 if 27 s1 K1 s Re s 0 J Vln2 x - 1 if 0 x e 1 o if e 1 x 28 Kv s Re s 0 cosh v arccosh -ln x f n Vln2 x- 1 I 0 11 . av . if c1 X 29 s Kv s Re s 0 sinhlv arccosh - 1 v I 0 ln x if 0 x e1 if c1 X 30
