reversion of

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11—18 of 18 matching pages

11: Bibliography D

… ►

T. M. Dunster (2001c) Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions. SIAM J. Math. Anal. 32 (5), pp. 987–1013.

ⓘ

External Links:: ISSN 0036-1410, Document, MathReview (Hasan Taşeli), ZentralBlatt
Referenced by:: §10.49(ii), §18.34(iii).
Encodings:: BibTeX

…

12: 3.7 Ordinary Differential Equations

… ►Similarly, if

w(z)

is decaying at least as fast as all other solutions along

\mathscr{P}

, then we may reverse the labeling of the

z_{j}

along

\mathscr{P}

and begin with initial values

w(b)

and

w^{\prime}(b)

. …

13: 22.19 Physical Applications

… ►With the same initial conditions, if the sign of gravity is reversed then the new period is

4{K^{\prime}}\left(\sin\left(\frac{1}{2}\alpha\right)\right)

; see Whittaker (1964, §44). …

14: 15.6 Integral Representations

… ►However, this reverses the direction of the integration contour, and in consequence (15.6.5) would need to be multiplied by

-1

. …

15: 18.33 Polynomials Orthogonal on the Unit Circle

… ►with complex coefficients

c_{k}

and of a certain degree

n

define the reversed polynomial

p^{*}(z)

by …

16: 2.7 Differential Equations

… ►The first of these references includes extensions to complex variables and reversions for zeros. …

17: 17.6 ${{}_{2}\phi_{1}}$ Function

… ►This reverses the order of summation in (17.6.2): …

There has been disagreement about the identification of the Chebyshev polynomials of the third and fourth kinds, denoted $V_{n}\left(x\right)$ and $W_{n}\left(x\right)$ , in published references. Originally, DLMF used the definitions given in (Andrews et al., 1999, Remark 2.5.3). However, those definitions were the reverse of those used by Mason and Handscomb (2003), Gautschi (2004) following Mason (1993) and Gautschi (1992), as was noted in several warnings added in Version 1.0.10 (August 7, 2015) of the DLMF. Since the latter definitions are more widely established, the DLMF is now adopting the definitions of Mason and Handscomb (2003). Essentially, what we previously denoted $V_{n}(x)$ is now written as $W_{n}(x)$ , and vice-versa.

This notational interchange necessitated changes in Tables 18.3.1, 18.5.1, and 18.6.1, and in Equations (18.5.3), (18.5.4), (18.7.5), (18.7.6), (18.7.17), (18.7.18), (18.9.11), and (18.9.12).

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