# Symbolic representation of bessel series derivative

I want to get symbolic expression for BesselJ derivative, where BesselJ is represented as series:

D[Sum[((-1)^k/(Gamma[k + ν + 1] k!)) (z/2)^(2 k + ν), {k, 0, Infinity}], z]


but I get following:

1/2 (BesselJ[-1 + ν, z] - BesselJ[1 + ν, z])


How to get derivative of this series in explicit form?

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Each term is D[((-1)^k/(Gamma[k + \[Nu] + 1] k!)) (z/2)^(2 k + \[Nu]), z]` –  belisarius Nov 21 '13 at 16:17
O. Thank you so much –  Bikineev Nov 21 '13 at 16:24