Expansion Problems Arising From the Watson Transformation
Expansion Problems Arising From the Watson Transformation
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V)yq. (y)dy ^1^^'^) + 2 sin nv / G(y. Z)i^(z, v)zg(z)dz f(y)'iy J(y;>v)y'' = Y (x, v) r 4 ^ (. 1 ^l(y, v)f(y) X '^(yjv)y' 2 2 sin rtv 2 ^o(^^^) f(y)dy r '^(y^v)y'' X / G(y, z)i^(z, v)zq(z)dz 2 sin jtv G(x, y)^„(y, v)yq(y)dy 'i-^(y, v)fiy)dy X wl (y;. V)y'' + - h sin^jtv f G(x, y)i (y, v)yq(y)dy . R ^^^^^ T G(y, z)? ( z, v)zq(z)dz a '^(y'^)y a = |^+$2+$5+li, • 27 We note that r ^. (y, v)f(y) J^=^^(x, v) / -i- -5- dy "^(y. V)y . A.
^l(y, v)f(y) u(y^v)y dy which was considered in proof of Theorem ...1. Hence lim — r / ^ ^ vdv = m — > 00 f(x) 2 m We will now show that the contributions to the contour integral due to Jp, ^ and ^, tend toward zero. Consider X y I2 =F-iI^ V-'^) / rr^ / G(y, . Z)?^(z, v)z 00 m Similarly ve find fel 2 2 h sin jtv G(x, y)5'Jy, v)yq(y)dy r f(y)dy " ^a^y. V)y ^ 2 / G(y, z)Y^(z, v)zq(z)dz const for V along r^ const, J{ev M^^ for V along r^ and 15; 2 sin 3tv G(x, y)T, (y, v)yq(y)dy / \(y, v)f(y)dy '^(y^-vjy const for V along P, const . J^ev 5 M«^ for V along r 2* 30 - We conclude therefore lim / ( ^, + ^)vdv = 0.
What to read after Expansion Problems Arising From the Watson Transformation?
You can find similar books in the "Read Also" column, or choose other free books by Eugene Pflumm to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
V)yq. (y)dy ^1^^'^) + 2 sin nv / G(y. Z)i^(z, v)zg(z)dz f(y)'iy J(y;>v)y'' = Y (x, v) r 4 ^ (. 1 ^l(y, v)f(y) X '^(yjv)y' 2 2 sin rtv 2 ^o(^^^) f(y)dy r '^(y^v)y'' X / G(y, z)i^(z, v)zq(z)dz 2 sin jtv G(x, y)^„(y, v)yq(y)dy 'i-^(y, v)fiy)dy X wl (y;. V)y'' + - h sin^jtv f G(x, y)i (y, v)yq(y)dy . R ^^^^^ T G(y, z)? ( z, v)zq(z)dz a '^(y'^)y a = |^+$2+$5+li, • 27 We note that r ^. (y, v)f(y) J^=^^(x, v) / -i- -5- dy "^(y. V)y . A.
^l(y, v)f(y) u(y^v)y dy which was considered in proof of Theorem ...1. Hence lim — r / ^ ^ vdv = m — > 00 f(x) 2 m We will now show that the contributions to the contour integral due to Jp, ^ and ^, tend toward zero. Consider X y I2 =F-iI^ V-'^) / rr^ / G(y, . Z)?^(z, v)z 00 m Similarly ve find fel 2 2 h sin jtv G(x, y)5'Jy, v)yq(y)dy r f(y)dy " ^a^y. V)y ^ 2 / G(y, z)Y^(z, v)zq(z)dz const for V along r^ const, J{ev M^^ for V along r^ and 15; 2 sin 3tv G(x, y)T, (y, v)yq(y)dy / \(y, v)f(y)dy '^(y^-vjy const for V along P, const . J^ev 5 M«^ for V along r 2* 30 - We conclude therefore lim / ( ^, + ^)vdv = 0.
What to read after Expansion Problems Arising From the Watson Transformation?
You can find similar books in the "Read Also" column, or choose other free books by Eugene Pflumm to read onlineMoreLess
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