���������cases���������������������������CXFK69���FlcVeurm

SearchAdvancedHelp

(0.001 seconds)

1—10 of 289 matching pages

1: 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). …

2: 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. …

3: 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. …

4: 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. …

5: 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. …

6: 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).

7: 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). …

8: 16.25 Methods of Computation

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

9: 22.22 Software

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

10: 18.32 OP’s with Respect to Freud Weights

… ►Of special interest are the cases $Q(x)=x^{2m}$, $m=1,2,\mathrm{\dots }$, and the case $Q(x)=\frac{1}{4}{x}^4-t{x}^2$ ($t\in ℝ$), see §32.15. …For a uniform asymptotic expansion in terms of Airy functions (§9.2) for the OP’s in the case $Q(x)=x^4$ see Bo and Wong (1999). … ►The case $Q(x)={\left|x\right|}^{\beta }$ ($\beta >0$) was already introduced by Freud (1976). The special case $Q(x)=\frac{1}{4}{x}^4-t{x}^2$ is of particular interest, see Clarkson and Jordaan (2018). …