# Generating DifferenceRoot Equation

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