# extended

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## 1—10 of 74 matching pages

##### 1: Foreword

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►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

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►The uniform asymptotic approximations given in §14.15 for ${P}_{\nu}^{-\mu}\left(x\right)$ and ${\bm{Q}}_{\nu}^{\mu}\left(x\right)$ 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).
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##### 3: Preface

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►Thus the utilitarian value of the Handbook will be extended far beyond its original scope and the traditional limitations of printed media.
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##### 4: 24.20 Tables

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►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.
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##### 5: 26.21 Tables

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►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 $p(\mathcal{D},n)$ for $n$ up to 500.
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##### 6: 27.6 Divisor Sums

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►Sums of number-theoretic functions extended over divisors are of special interest.
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►Generating functions, Euler products, and Möbius inversion are used to evaluate many sums extended over divisors.
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##### 7: 4.1 Special Notation

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►The main purpose of the present chapter is to extend these definitions and properties to complex arguments $z$.
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##### 8: 25.18 Methods of Computation

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►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 $\zeta \left(\frac{1}{2}+\mathrm{i}t\right)$.
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##### 9: 27.1 Special Notation

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

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##### 10: 33.13 Complex Variable and Parameters

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►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).
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