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Tables of Bessel Transforms F. Oberhettinger

Tables of Bessel Transforms

F. Oberhettinger

Published January 1st 1972
ISBN : 9783540059974
Paperback
304 pages
Enter the sum

 About the Book 

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)MoreThis 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.