pseudo-lemniscatic case

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1: 23.5 Special Lattices

… ►This happens in the cases treated in the following four subsections. … ►

§23.5(iii) Lemniscatic Lattice

… ►

§23.5(iv) Rhombic Lattice

… ► $e_1$ and $g_3$ have the same sign unless $2{\omega }_3=(1+\mathrm{i}){\omega }_1$ when both are zero: the pseudo-lemniscatic case. As a function of $\mathrm{\Im }{e}_3$ the root $e_1$ is increasing. …

2: 23.23 Tables

… ►2 in Abramowitz and Stegun (1964) gives values of $\mathrm{\wp }\left(z\right)$, ${\mathrm{\wp }}^{\prime }\left(z\right)$, and $\zeta \left(z\right)$ to 7 or 8D in the rectangular and rhombic cases, normalized so that ${\omega }_1=1$ and ${\omega }_3=\mathrm{i}a$ (rectangular case), or ${\omega }_1=1$ and ${\omega }_3=\frac{1}{2}+\mathrm{i}a$ (rhombic case), for $a$ = 1. …05, and in the case of $\mathrm{\wp }\left(z\right)$ the user may deduce values for complex $z$ by application of the addition theorem (23.10.1). …

3: 18.31 Bernstein–Szegő Polynomials

… ►In consequence, $p_n(\cos \theta )$ can be given explicitly in terms of $\rho (\cos \theta )$ and sines and cosines, provided that in the first case, in the second case, and in the third case. …

4: 12.18 Methods of Computation

… ►Because PCFs are special cases of confluent hypergeometric functions, the methods of computation described in §13.29 are applicable to PCFs. …

5: 17.16 Mathematical Applications

… ►Many special cases of $q$-series arise in the theory of partitions, a topic treated in §§27.14(i) and 26.9. …

6: 16.18 Special Cases

§16.18 Special Cases

►The ${}_1{}^{}F_1^{}$ and ${}_2{}^{}F_1^{}$ functions introduced in Chapters 13 and 15, as well as the more general ${}_p{}^{}F_q^{}$ functions introduced in the present chapter, are all special cases of the Meijer $G$-function. …As a corollary, special cases of the ${}_1{}^{}F_1^{}$ and ${}_2{}^{}F_1^{}$ functions, including Airy functions, Bessel functions, parabolic cylinder functions, Ferrers functions, associated Legendre functions, and many orthogonal polynomials, are all special cases of the Meijer $G$-function. …

7: 12.1 Special Notation

… ►Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values. … ►Whittaker’s notation $D_{\nu }\left(z\right)$ is useful when $\nu$ is a nonnegative integer (Hermite polynomial case).

8: Possible Errors in DLMF

… ►There are also cases where browser bugs or poor fonts can be misleading; you can verify MathML display by comparing the to the images or TeXfound under Encodings in the Info boxes (see About MathML). …

9: 16.25 Methods of Computation

… ►In these cases integration, or recurrence, in either a forward or a backward direction is unstable. …

10: 22.22 Software

… ►However, in some cases no research software has been found. …