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The Pearson equation and the beta integrals. (English) Zbl 0808.33002

The Pearson equation is the first order linear, homogeneous differential equation with polynomial coefficients, the derivative multiplied by a second degree polynomial, and the other polynomial linear. K. Pearson was interested in this as a way of doing the various beta integrals and their limits all at once.
There are other beta type integrals, of Mellin-Barnes types, of Ramanujan type, sum analogues, and many \(q\)-extensions. Many of the known one dimensional beta and \(q\)-beta integrals and sums are treated by a common method in this paper. Some new ones are also obtained.
Reviewer: R.Askey (Madison)

MSC:

33B15 Gamma, beta and polygamma functions
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