KelvinKei[n, z] == (1/8) (4 (-I)^(n + 1) BesselK[n, (-1)^(1/4) z] - 2 (-1)^n I Pi BesselY[n, (-1)^(1/4) z] - (-1)^n I BesselJ[n, (-1)^(1/4) z] ((-I) Pi + 4 Log[z] - 4 Log[(-1)^(1/4) z]) - I^(n + 1) BesselI[n, (-1)^(1/4) z] ((-I) Pi - 4 Log[z] + 4 Log[(-1)^(1/4) z]) - (-1)^n I n! Sum[((2^(1 - k + n) I^((k - n)/2) z^(k - n))/((k - n) k!)) ((-1)^k I^n BesselI[k, (-1)^(1/4) z] - BesselJ[k, (-1)^(1/4) z]), {k, 0, n - 1}] - ((I 2^(1 - n) E^((3 I n Pi)/4) z^n)/n!) Sum[(1/j) (I^n HypergeometricPFQ[{j}, {1 + j, 1 + n}, -((I z^2)/4)] - HypergeometricPFQ[{j}, {1 + j, 1 + n}, (I z^2)/4]), {j, 1, n}] + I^(n + 1) Sum[(2^(1 - 2 k + n) I^(k - n/2) (-(-1)^(k + n) + I^n) (n - k - 1)! z^(2 k - n))/k!, {k, 0, n - 1}]) /; Element[n, Integers] && n >= 0

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2007-05-02