D[KelvinKer[z], {z, n}] == 2^(-1 - 3 (n/2)) (I - 1)^n Sum[(((1 + n) Binomial[n, 2 k])/(1 + 2 k)) ((I - I^(n + 1)) KelvinKei[4 k - n, z] + (1 + I^n) KelvinKer[4 k - n, z]) - (1/z) (1 + I) Sqrt[2] (1 + 4 k - n) Binomial[n, 1 + 2 k] ((-I + I^n) KelvinKei[1 + 4 k - n, z] + (-1 + I^(n + 1)) KelvinKer[1 + 4 k - n, z]), {k, 0, Floor[n/2]}] /; Element[n, Integers] && n >= 0

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2007-05-02