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1: Foreword

… ►The document you are now holding, or the Web page you are now reading, represents an effort to extend the legacy of A&S well into the 21st century. The new printed volume, the NIST Handbook of Mathematical Functions, serves a similar function as the original A&S, though it is heavily updated and extended. …

2: 14.26 Uniform Asymptotic Expansions

… ►The uniform asymptotic approximations given in §14.15 for $P_{\nu }^{-\mu }\left(x\right)$ and ${𝑸}_{\nu }^{\mu }\left(x\right)$ for are extended to domains in the complex plane in the following references: §§14.15(i) and 14.15(ii), Dunster (2003b); §14.15(iii), Olver (1997b, Chapter 12); §14.15(iv), Boyd and Dunster (1986). …

3: Preface

… ►Thus the utilitarian value of the Handbook will be extended far beyond its original scope and the traditional limitations of printed media. …

4: 24.20 Tables

… ►In Wagstaff (2002) these results are extended to $n=60(2)152$ and $n=40(2)88$, respectively, with further complete and partial factorizations listed up to $n=300$ and $n=200$, respectively. …

5: 26.21 Tables

… ►Abramowitz and Stegun (1964, Chapter 24) tabulates binomial coefficients $\left(\genfrac{}{}{0.0pt}{}{m}{n}\right)$ for $m$ up to 50 and $n$ up to 25; extends Table 26.4.1 to $n=10$; tabulates Stirling numbers of the first and second kinds, $s(n,k)$ and $S(n,k)$, for $n$ up to 25 and $k$ up to $n$; tabulates partitions $p\left(n\right)$ and partitions into distinct parts $p(𝒟,n)$ for $n$ up to 500. …

6: 27.6 Divisor Sums

… ►Sums of number-theoretic functions extended over divisors are of special interest. … ►Generating functions, Euler products, and Möbius inversion are used to evaluate many sums extended over divisors. …

7: 4.1 Special Notation

… ►The main purpose of the present chapter is to extend these definitions and properties to complex arguments $z$. …

8: 25.18 Methods of Computation

… ►The principal tools for computing $\zeta \left(s\right)$ are the expansion (25.2.9) for general values of $s$, and the Riemann–Siegel formula (25.10.3) (extended to higher terms) for $\zeta \left(\frac{1}{2}+\mathrm{i}t\right)$. …

9: 27.1 Special Notation

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$d,k,m,n$	positive integers (unless otherwise indicated).
…
${\sum }_p$, ${\prod }_p$	sum, product extended over all primes.
…

10: 33.13 Complex Variable and Parameters

… ►The functions $F_{\mathrm{\ell }}(\eta ,\rho )$, $G_{\mathrm{\ell }}(\eta ,\rho )$, and $H_{\mathrm{\ell }}^{\pm }(\eta ,\rho )$ may be extended to noninteger values of $\mathrm{\ell }$ by generalizing $(2\mathrm{\ell }+1)!=\mathrm{\Gamma }\left(2\mathrm{\ell }+2\right)$, and supplementing (33.6.5) by a formula derived from (33.2.8) with $U(a,b,z)$ expanded via (13.2.42). …