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31: 29.15 Fourier Series and Chebyshev Series

… ►A convenient way of constructing the coefficients, together with the eigenvalues, is as follows. …

32: Bibliography H

… ►

Applied and Computational Complex Analysis. Vol. 3: Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons Inc.], New York.

ⓘ

Notes:

Reprinted in 1993.

External Links:

ISBN 0-471-08703-3; 0-471-58986-1, MathReview (A. E. Heins), ZentralBlatt

Referenced by:

§1.14(v), Ch.3.

Encodings:

BibTeX

…

33: Mathematical Introduction

… ►For all equations and other technical information this Handbook and the DLMF either provide references to the literature for proof or describe steps that can be followed to construct a proof. …

34: 2.9 Difference Equations

… ►The construction fails if ${\rho }_1={\rho }_2$, that is, when $f_0^2=4g_0$. …

35: 9.11 Products

… ►Numerically satisfactory triads of solutions can be constructed where needed on $ℝ$ or $ℂ$ by inspection of the asymptotic expansions supplied in §9.7. …

36: 13.7 Asymptotic Expansions for Large Argument

… ►Corresponding error bounds for (13.7.2) can be constructed by combining (13.2.41) with (13.7.4)–(13.7.9). …

37: 16.3 Derivatives and Contiguous Functions

… ►Other versions of these identities can be constructed with the aid of the operator identity …

38: 23.20 Mathematical Applications

… ►The geometric nature of this construction is illustrated in McKean and Moll (1999, §2.14), Koblitz (1993, §§6, 7), and Silverman and Tate (1992, Chapter 1, §§3, 4): each of these references makes a connection with the addition theorem (23.10.1). …

39: 31.3 Basic Solutions

… ►When $\gamma \in \mathbb{Z}$, linearly independent solutions can be constructed as in §2.7(i). …

40: 33.12 Asymptotic Expansions for Large $\eta$

… ►Then, by application of the results given in §§2.8(iii) and 2.8(iv), two sets of asymptotic expansions can be constructed for $F_{\mathrm{\ell }}(\eta ,\rho )$ and $G_{\mathrm{\ell }}(\eta ,\rho )$ when $\eta \to \mathrm{\infty }$. …