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11: 8.1 Special Notation
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►Unless otherwise indicated, primes denote derivatives with respect to the argument.
►The functions treated in this chapter are the incomplete gamma functions , , , , and ; the incomplete beta functions and ; the generalized exponential integral ; the generalized sine and cosine integrals , , , and .
►Alternative notations include: Prym’s functions
, , Nielsen (1906a, pp. 25–26), Batchelder (1967, p. 63); , , Dingle (1973); , , Magnus et al. (1966); , , Luke (1975).
12: 16.6 Transformations of Variable
13: 17.15 Generalizations
§17.15 Generalizations
…14: 16.4 Argument Unity
15: 7.16 Generalized Error Functions
§7.16 Generalized Error Functions
►Generalizations of the error function and Dawson’s integral are and . …16: Sidebar 5.SB1: Gamma & Digamma Phase Plots
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►This pattern is analogous to one that would be seen in fluid flow generated by a semi-infinite line of vortices.
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►The fluid flow analogy in this case involves a line of vortices of alternating sign of circulation, resulting in a near cancellation of flow far from the real axis.
17: David M. Bressoud
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►His books are Analytic and Combinatorial
Generalizations of the Rogers-Ramanujan Identities, published in Memoirs of the American Mathematical Society 24, No.
227, in 1980, Factorization and Primality Testing, published by Springer-Verlag in 1989, Second Year Calculus from Celestial Mechanics to Special
Relativity, published by Springer-Verlag in 1992, A Radical
Approach to Real Analysis, published by the Mathematical Association of America in 1994, with a second edition in 2007, Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, published by the Mathematical Association of America and Cambridge University Press in 1999, A Course in Computational Number Theory (with S.
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18: Barry I. Schneider
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►He is also a General Editor for the DLMF project.
…Before coming to NIST in 2014, he was a postdoctoral research associate at the University of Southern California (1969-1970), and a staff member of the General Telephone and Electronics Laboratory (1970-1972).
…In early 2014, he came to NIST as General Editor of the DLMF project.
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►He was a visiting scientist at NIST from 1995 to 2013 and spent a sabbatical year at NIST in 2000-2001.
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19: Errata
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Subsection 25.10(ii)
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General
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Equation (14.2.7)
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Equation (10.13.4)
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Table 18.3.1
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In the paragraph immediately below (25.10.4), it was originally stated that “more than one-third of all zeros in the critical strip lie on the critical line.” which referred to Levinson (1974). This sentence has been updated with “one-third” being replaced with “41%” now referring to Bui et al. (2011) (suggested by Gergő Nemes on 2021-08-23).
Several biographies had their publications updated.
The Wronskian was generalized to include both associated Legendre and Ferrers functions.
has been generalized to cover an additional case.
Special cases of normalization of Jacobi polynomials for which the general formula is undefined have been stated explicitly in Table 18.3.1.