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Is there any identity/formula for reducing/increasing the power in the parameters of the Gauss Hypergeometric function $ _2F_1(a,b;c;z^d)$ (d is a real) let's say to z?

Is there also any identity for doing the same for the Kummer Confluent Hypergeometric function $ _1F_1(a;c;z^d)$?

In addition, is there any identity connecting both functions without including integrals?

Thanks in advance

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