resolvent cubic

(0.001 seconds)

11—20 of 31 matching pages

11: 20.1 Special Notation

$m$ , $n$	integers.
…
$q^{\alpha}$	$e^{i\alpha\pi\tau}$ for $\alpha\in\mathbb{R}$ (resolving issues of choice of branch).
…

…

12: 23.21 Physical Applications

… ►The Weierstrass function

\wp

plays a similar role for cubic potentials in canonical form

g_{3}+g_{2}x-4x^{3}

. …

13: 10.74 Methods of Computation

… ►Newton’s rule is quadratically convergent and Halley’s rule is cubically convergent. …

14: 19.14 Reduction of General Elliptic Integrals

… ►The choice among 21 transformations for final reduction to Legendre’s normal form depends on inequalities involving the limits of integration and the zeros of the cubic or quartic polynomial. …

15: 31.7 Relations to Other Functions

… ►They are analogous to quadratic and cubic hypergeometric transformations (§§15.8(iii)–15.8(v)). …

16: Bibliography R

… ►

W. H. Reid (1997a) Integral representations for products of Airy functions. II. Cubic products. Z. Angew. Math. Phys. 48 (4), pp. 646–655.

ⓘ

External Links:: ISSN 0044-2275, Document, MathReview (E. R. Love), ZentralBlatt
Referenced by:: (9.11.16), (9.11.17), §9.11(iii), §9.11(v).
Encodings:: BibTeX

…

17: 4.21 Identities

… ►In (4.21.21)–(4.21.23) Table 4.16.1 and analytic continuation will assist in resolving sign ambiguities. …

18: 28.4 Fourier Series

… ►Ambiguities in sign are resolved by (28.4.13)–(28.4.16) when

q=0

, and by continuity for the other values of

q

. …

19: 28.31 Equations of Whittaker–Hill and Ince

… ►ambiguities in sign being resolved by requiring

C_{p}^{m}(x,\xi)

and

{S_{p}^{m}}^{\prime}(x,\xi)

to be continuous functions of

x

and positive when

x=0

. …

20: Bibliography W

… ►

G. N. Watson (1910) The cubic transformation of the hypergeometric function. Quart. J. Pure and Applied Math. 41, pp. 70–79.

ⓘ

External Links:: ZentralBlatt
Referenced by:: §15.8(v), §15.8(v).
Encodings:: BibTeX

…