Expansion Problems Arising From the Watson Transformation
Expansion Problems Arising From the Watson Transformation
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In our eReader you can find the full English version of the book. Read Expansion Problems Arising From the Watson Transformation Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book 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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