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31: Errata

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The title of the paragraph which was previously “Andrews’ Terminating $q$-Analog of (17.7.8)” has been changed to “Andrews’ $q$-Analog of the Terminating Version of Watson’s ${}_3{}^{}F_2^{}$ Sum (16.4.6)”. The title of the paragraph which was previously “Andrews’ Terminating $q$-Analog” has been changed to “Andrews’ $q$-Analog of the Terminating Version of Whipple’s ${}_3{}^{}F_2^{}$ Sum (16.4.7)”.

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17.9.3 $${}_2{}^{}\varphi _1^{}(\genfrac{}{}{0pt}{}{a,b}{c};q,z)=\frac{{(abz/c;q)}_{\mathrm{\infty }}}{{(bz/c;q)}_{\mathrm{\infty }}}{}_3{}^{}\varphi _2^{}(\genfrac{}{}{0pt}{}{a,c/b,0}{c,cq/(bz)};q,q)+\frac{{(a,bz,c/b;q)}_{\mathrm{\infty }}}{{(c,z,c/(bz);q)}_{\mathrm{\infty }}}{}_3{}^{}\varphi _2^{}(\genfrac{}{}{0pt}{}{z,abz/c,0}{bz,bzq/c};q,q)$$

Originally, the second term on the right-hand side was missing. The form of the equation where the second term is missing is correct if the ${}_2{}^{}\varphi _1^{}$ is terminating. It is this form which appeared in the first edition of Gasper and Rahman (1990). The more general version which appears now is what is reproduced in Gasper and Rahman (2004, (III.5)).

Reported by Roberto S. Costas-Santos on 2019-04-26

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Confluent hypergeometric functions were incorrectly linked to the definitions of the Kummer confluent hypergeometric and parabolic cylinder functions. However, to the eye, the functions appeared correct. The links were corrected.

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The Weierstrass zeta function was incorrectly linked to the definition of the Riemann zeta function. However, to the eye, the function appeared correct. The link was corrected.

… ►The Handbook of Mathematical Functions was published, and the Digital Library of Mathematical Functions was released.

32: 29.3 Definitions and Basic Properties

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§29.3(i) Eigenvalues

… ►If $\nu$ is a nonnegative integer and $2p\le \nu$, then the continued fraction on the right-hand side of (29.3.10) terminates, and (29.3.10) has only the solutions (29.3.9) with $2m\le \nu$. … ►

§29.3(iv) Lamé Functions

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§29.3(v) Normalization

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§29.3(vi) Orthogonality

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33: 18.28 Askey–Wilson Class

… ►Both the Askey–Wilson polynomials and the $q$-Racah polynomials can best be described as functions of $z$ (resp. … ►For the notation of $q$-hypergeometric functions see §§17.2 and 17.4(i). ►

§18.28(ii) Askey–Wilson Polynomials

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§18.28(viii) $q$-Racah Polynomials

… ►Genest et al. (2016) showed that these polynomials coincide with the nonsymmetric Wilson polynomials in Groenevelt (2007).