This material represents a collection of integral tra- forms
involving Bessel (or related) functions as kernel. The following
types of inversion formulas have been singled out. k I. g(y) = f
(x) (xy) 2J (xy) dx J V 0 k I' . f (x) g (y) (xy) 2J (xy) dy J V 0
II. g(y) f(x) (XY)~K (xy)dx J v 0 c+ioo k 1 II'. f (x) = g (y) (xy)
2 [Iv (xy) + I_v(xy)]dy J 27fT c-ioo or also c+ioo k 1 II". f(x) =
g (y) (xy) 2Iv (xy) dx J rri oo c-i k III. g(y) f(x) (xy) 2y (xy)
dx + J v 0 k III' . f(x) g(y) (xy) "1lv (xy) dy J 0 k IV. g(y) f
(x) (xy) "Kv (xy) dx J 0 k g(y) (xy) 2Y (xy)dy IV' * f(x) J v 0 V
Preface V. g(y) f(X)Kix(y)dx J 0 -2 -1 sinh (7TX) V'. f(x) 27T x
g(y)y Kix(y)dy J 0 21-~[r(~~+~-~v)r(~~+~+~v)]-1 VI. g(y) . J f (x)
(xy) ~s (xy) dx o ~,v l-~ -1 VI' . f(x) 2 [r (~~+~-~v) r (~~+~+~v)
] * * J -5 (xy)]dy g(y) (XY)~[S~,v(xy) ~,v 0 [xy)~]dX VII. g(y)
f(x)\ ~ J 0 0 VII' * f(x) g(y) \ [(xy) lz]dy ~ f 0 0 with \ (z) o
(For notations and definitions see the appendix of this book. ) The
transform VII is also known as the divisor transform.
General
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