Watson identities

SearchAdvancedHelp

(0.001 seconds)

1—10 of 15 matching pages

1: 20.7 Identities

… ►

§20.7(v) Watson’s Identities

…

2: 6.12 Asymptotic Expansions

…

3: 7.12 Asymptotic Expansions

…

4: 23.10 Addition Theorems and Other Identities

§23.10 Addition Theorems and Other Identities

… ►For further addition-type identities for the $\sigma$-function see Lawden (1989, §6.4). … ►For these results and further identities see Lawden (1989, §6.6) and Apostol (1990, p. 14).

5: 22.6 Elementary Identities

§22.6 Elementary Identities

… ►See §22.17.

6: 20.2 Definitions and Periodic Properties

… ►

20.2.10 $$M\equiv M(z|\tau )={\mathrm{e}}^{\mathrm{i}z+(\mathrm{i}\pi \tau /4)},$$

ⓘ

Defines:

$M$ (locally)

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\equiv$: equals by definition, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $z$: complex and $\tau$: lattice parameter

A&S Ref:

16.33.1 (in different notation)

Permalink:

http://dlmf.nist.gov/20.2.E10

Encodings:

pMML, png, TeX

See also:

Annotations for §20.2(iii), §20.2 and Ch.20

…

7: 20.4 Values at $z$ = 0

… ►

Jacobi’s Identity

…

8: 1.13 Differential Equations

… ►Then the following relation is known as Abel’s identity … ►

Cayley’s Identity

… ►For a regular Sturm-Liouville system, equations (1.13.26) and (1.13.29) have: (i) identical eigenvalues, $\lambda$; (ii) the corresponding (real) eigenfunctions, $u(x)$ and $w(t)$, have the same number of zeros, also called nodes, for $t\in (0,c)$ as for $x\in (a,b)$; (iii) the eigenfunctions also satisfy the same type of boundary conditions, un-mixed or periodic, for both forms at the corresponding boundary points. …

9: 22.8 Addition Theorems

… ►A geometric interpretation of (22.8.20) analogous to that of (23.10.5) is given in Whittaker and Watson (1927, p. 530). … ►For these and related identities see Copson (1935, pp. 415–416). …

10: Bibliography W

… ►

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

►

Generating functions of class-numbers. Compositio Math. 1, pp. 39–68.

ⓘ

External Links:

ISSN 0010-437X, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§20.7(v), §20.8.

Encodings:

BibTeX

►

The surface of an ellipsoid. Quart. J. Math., Oxford Ser. 6, pp. 280–287.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§19.33(i).

Encodings:

BibTeX

►

Two tables of partitions. Proc. London Math. Soc. (2) 42, pp. 550–556.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§27.21.

Encodings:

BibTeX

… ►

A table of Ramanujan’s function $\tau (n)$ . Proc. London Math. Soc. (2) 51, pp. 1–13.

ⓘ

External Links:

Document, MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§27.21.

Encodings:

BibTeX

…