Comments to the book by W. N. Bailey, Generalized hypergeometric series

Comments to the book by W. N. Bailey, Generalized hypergeometric series

February 8, 2006 | T. H. Koornwinder
This section contains errata and comments for the book "Generalized Hypergeometric Series" by W. N. Bailey, published by Cambridge University Press in 1935 and reprinted by Hafner in 1972. The errata were communicated by George Gasper and include: 1. On page 32, §4.5, formula (1), the first line should skip the lower semicolon. 2. On page 93, 1.3, a formula for \( n = 2 \) is provided, which yields a specific expression involving Gamma functions. This formula is then used to derive a Taylor series expansion at \( z = 1 \), leading to a general identity for \( _3F_2 \) hypergeometric series. This identity also applies to the paper by T. H. Koornwinder, where it replaces identities (2.5), (5.3), and (5.4) with \( N = 0 \). 3. On page 95, §10.4, formula (7), several corrections are made to the denominators: - Replace \( (v + n - 1)(w + n - 1) \) with \( \Gamma(v + n - 1)\Gamma(w + n - 1) \). - Replace \( \Gamma(v + n - 1) \) with \( (v + n - 1) \). - Replace \( \Gamma(w + n - 1) \) with \( (w + n - 1) \). These corrections ensure the accuracy of the formulas and identities presented in the book.This section contains errata and comments for the book "Generalized Hypergeometric Series" by W. N. Bailey, published by Cambridge University Press in 1935 and reprinted by Hafner in 1972. The errata were communicated by George Gasper and include: 1. On page 32, §4.5, formula (1), the first line should skip the lower semicolon. 2. On page 93, 1.3, a formula for \( n = 2 \) is provided, which yields a specific expression involving Gamma functions. This formula is then used to derive a Taylor series expansion at \( z = 1 \), leading to a general identity for \( _3F_2 \) hypergeometric series. This identity also applies to the paper by T. H. Koornwinder, where it replaces identities (2.5), (5.3), and (5.4) with \( N = 0 \). 3. On page 95, §10.4, formula (7), several corrections are made to the denominators: - Replace \( (v + n - 1)(w + n - 1) \) with \( \Gamma(v + n - 1)\Gamma(w + n - 1) \). - Replace \( \Gamma(v + n - 1) \) with \( (v + n - 1) \). - Replace \( \Gamma(w + n - 1) \) with \( (w + n - 1) \). These corrections ensure the accuracy of the formulas and identities presented in the book.
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