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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 ν - μ ( x ) and Q ν μ ( x ) for 1 < x < 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 ( m n ) 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 ( n ) 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 ζ ( s ) are the expansion (25.2.9) for general values of s , and the Riemann–Siegel formula (25.10.3) (extended to higher terms) for ζ ( 1 2 + i t ) . …
9: 27.1 Special Notation
d , k , m , n positive integers (unless otherwise indicated).
p , p sum, product extended over all primes.
10: 33.13 Complex Variable and Parameters
The functions F ( η , ρ ) , G ( η , ρ ) , and H ± ( η , ρ ) may be extended to noninteger values of by generalizing ( 2 + 1 ) ! = Γ ( 2 + 2 ) , and supplementing (33.6.5) by a formula derived from (33.2.8) with U ( a , b , z ) expanded via (13.2.42). …