construct the regular Gamma-function representation of a hypergeometric term
hypergeometric term of n
Let H be a hypergeometric term of n, R be the certificate of H, and n0 be an integer such that R has neither a pole nor a zero for all n0≤n. The RegularGammaForm(H,n) calling sequence returns the multiplicative decomposition of the form H⁡n0⁢∏k=n0n−1⁡R⁡k where the product is expressed in terms of a product of the Gamma function of the form Γ⁡n−c where c is a constant and their reciprocals.
H ≔ ∏k=1n−11⁢3⁢k2+6⁢k+4⁢2⁢k+3⁢4⁢k+5⁢k+1⁢4⁢k+32⁢k⁢4⁢k−1⁢2⁢k−1⁢4⁢k−3⁢2⁢k+5⁢k+2⁢3⁢k2+1
Compare the number of Gamma-function values returned from RegularGammaForm with that of any one of the four efficient representations of the input hypergeometric term H⁡n:
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