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By Gianni Gilardi

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53 ~ . [ (x2+a 2) ~+xl v-I -1 < Re v < 5/2 -k 211 2a v- 3/2 sinh(~aY)Kv_~(~ay) I. 61 1< - Re v < 5/2 _ n 2aV 3/2 [cos(~ay)Jv_~(~ay)- sin(~aY)Yv_~(~aY)l + 44 I. >0 m 1 ( - I'I m+1 Y ~+v d + {(al+yl)-~ dam+ 1 . 3 f k+v (a. +(0. >0 ~(1[ Z. ) L. I~v ( 80. ) 46 I. ::2 e ±iax 2 (2a)-v-l y v+\ exp [+. (v+l _l. 18 XV+k2exp [-a(b 2 +x 2 ) k2] Re v>-l, Re a>O --~~----------------~-------------------------------------- Re v>-l, Re a>O Re v>-l, Re a>O 48 I. Hankel Transfonns 00 f (x) g(y) = Jf 0 X~-V(b2+X2)-~ .

Br(l+v) . W, -~ Y M, ~'T, h zV h {b[(a 2+y2)2_a)} h h{b[(a 2+y2)2+ a )} -~T, 2'V . 72_~ 2 \ -'\1- 3/2 so I. 9 f o y>a o y I;; x ll- 3/2 sin (ax) l-Re v < Re 2 II < -v -V-ll. 10 2 xll _312 cos (ax) -Re v < Re II 2 < F 1 3 a2 (I;;+l;;ll+l;;v l;;+l;;ll-I;;v;-;--) ' 2 y2 , y > a -v -v-ll 1T r(V+ll) v+l< a cos[Z(v+ll)] r(v+l) y 2. 18 cos (ax) Re v > 2n - 5'2 n = 0,1,2, ... (_1)nlarrb2n-v-1e-abY~I v (by) y < a 52 I. 19 . :.. 20 . :.. :.. 27 - >,lTv) -1 < Re v<,. 25 53 x>a S4 1. 6 Trigonometric and Inverse Trigonometric Functions f (x) x Re v > -1 l< ~1Ty 'J v l< f g(y) = -% cos(ax)sin(bx-1 ) 55 f(x) (xy) 2JV (xy)dx o l< l< (cb') [J v (db 2) COS (~1TV) l< .

20 . :.. :.. 27 - >,lTv) -1 < Re v<,. 25 53 x>a S4 1. 6 Trigonometric and Inverse Trigonometric Functions f (x) x Re v > -1 l< ~1Ty 'J v l< f g(y) = -% cos(ax)sin(bx-1 ) 55 f(x) (xy) 2JV (xy)dx o l< l< (cb') [J v (db 2) COS (~1TV) l< . 37 - 3/2 l< - 3/2 sin (ax+bx Re v > -1 -1 l< ) y'J V (cb - l<2 ) [Jv(db ~ )COS(~1TV) - Yv(db~)sin(~1Tv)l y < a 56 I. 40 . sin[a(b 2+x z )1o] Re k k k = (a+y) 2± (a-y) 2 k Kv (db 2) Y < a I -1TyloJ (cblo) [J (dblo) sin (lo1Tv) + v v k k = (a+y) 2± (a-y) 2 Y < a I k k -lo1TY 2Jlov {lob [a- (a 2_yZ) 2] } Y {lob[a+(a z _y 2)1o]} -lov .

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