A hypergeometric series sum_k c_k is a series for which c_0 = 1 and the ratio of consecutive terms is a rational function of the summation index k, i.e., one for which c_(k + 1)/c_k = (P(k))/(Q(k)), with P(k) and Q(k) polynomials. In this case, c_k is called a hypergeometric term. The functions generated by hypergeometric series are called hypergeometric functions or, more generally, generalized hypergeometric functions.
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