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I like to find a difference root equation I use the following methods use for mathematica but I have not get any result Clear[p]

DifferenceRootReduce[(\[Pi]^(3/2)
   Gamma[3/2 + k] HypergeometricPFQ[{-(1/2), 1/2, 3/2 + k}, {1, 
    2 + k}, p])/(2 Gamma[2 + k]), k]

SeriesCoefficient[(\[Pi]^(3/2)
   Gamma[3/2 + k] HypergeometricPFQ[{-(1/2), 1/2, 3/2 + k}, {1, 
    2 + k}, p])/(2 Gamma[2 + k]), {p, 0, k}, Method -> "Holonomic"]

it is possible that Mathematica do not interpret the hypergeometric function cause maple does the difference equations thanks anyway

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