KelvinKei[\[Nu], z] == Subscript[F, Infinity][z, \[Nu]] /; Subscript[F, n][z, \[Nu]] == (-((z^\[Nu] Gamma[-\[Nu]])/2^(\[Nu] + 1))) Sum[(Sin[(1/4) Pi (\[Nu] - 2 k)]/(Pochhammer[\[Nu] + 1, k] k!)) (z/2)^(2 k), {k, 0, n}] - (Gamma[\[Nu]]/(z^\[Nu] 2^(-\[Nu] + 1))) Sum[(Sin[(1/4) Pi (3 \[Nu] - 2 k)]/(Pochhammer[1 - \[Nu], k] k!)) (z/2)^(2 k), {k, 0, n}] == KelvinKei[\[Nu], z] - ((-I)^n 2^(-4 - 2 n + \[Nu]) E^((3 I Pi \[Nu])/4) Pi z^(2 + 2 n - \[Nu]) Csc[Pi \[Nu]] HypergeometricPFQRegularized[{1}, {2 + n, 2 + n - \[Nu]}, -((I z^2)/4)] + (I^n 2^(-4 - 2 n + \[Nu]) Pi z^(2 + 2 n - \[Nu]) Csc[Pi \[Nu]] HypergeometricPFQRegularized[{1}, {2 + n, 2 + n - \[Nu]}, (I z^2)/4])/E^((3/4) I Pi \[Nu]) - (-I)^n 2^(-4 - 2 n - \[Nu]) E^((I Pi \[Nu])/4) Pi z^(2 + 2 n + \[Nu]) Csc[Pi \[Nu]] HypergeometricPFQRegularized[{1}, {2 + n, 2 + n + \[Nu]}, -((I z^2)/4)] - (I^n 2^(-4 - 2 n - \[Nu]) Pi z^(2 + 2 n + \[Nu]) Csc[Pi \[Nu]] HypergeometricPFQRegularized[{1}, {2 + n, 2 + n + \[Nu]}, (I z^2)/4])/E^((1/4) I Pi \[Nu])) && Element[n, Integers] && n >= 0

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2007-05-02