Lamé functions

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31: Bibliography W

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The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

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External Links:

ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt

Referenced by:

§29.19(ii).

Encodings:

BibTeX

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32: Bibliography S

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On integral representations for Lamé and other special functions. SIAM J. Math. Anal. 11 (4), pp. 702–723.

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External Links:

ISSN 0036-1410, Document, MathReview (R. K. Gupta), ZentralBlatt

Referenced by:

§29.17(i), §29.8.

Encodings:

BibTeX

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The expansion of Lamé functions into series of associated Legendre functions of the second kind. Proc. Cambridge Philos. Soc. 62, pp. 441–452.

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External Links:

Document, MathReview (F. M. Arscott), ZentralBlatt

Referenced by:

§29.17(i).

Encodings:

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Integral equations and relations for Lamé functions and ellipsoidal wave functions. Proc. Cambridge Philos. Soc. 64, pp. 113–126.

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External Links:

Document, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

§29.8.

Encodings:

BibTeX

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33: 31.18 Methods of Computation

… ►The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 28–30.

34: Bibliography

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Integral equations and relations for Lamé functions. Quart. J. Math. Oxford Ser. (2) 15, pp. 103–115.

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External Links:

Document, MathReview (I. Marx), ZentralBlatt

Referenced by:

§29.8.

Encodings:

BibTeX

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Periodic Differential Equations. An Introduction to Mathieu, Lamé, and Allied Functions. International Series of Monographs in Pure and Applied Mathematics, Vol. 66, Pergamon Press, The Macmillan Co., New York.

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§28.1, §28.1, §28.10(i), §28.11, §28.12(ii), §28.17, §28.2(ii), §28.2(iii), §28.2(iv), §28.28(i), §28.28(ii), §28.29(i), §28.32(i), §28.32(ii), §28.4(i), §28.5(i), Ch.28, §29.1, §29.11, §29.12(i), §29.12(ii), §29.12(iii), §29.14, §29.15(ii), §29.15(ii), §29.17(i), §29.18(iii), Ch.29, §30.1, §30.10, §30.11(i), §30.11(vi), §30.2(ii), §30.4(iii), §30.6, §30.8(i), §30.8(ii), Ch.30, §31.4, §31.5, §31.9(ii), Notations F, Notations G, Notations M, Notations N.

Encodings:

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35: 29.2 Differential Equations

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§29.2(ii) Other Forms

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29.2.4 $$(1-k^2{\cos }^2\varphi )\frac{d^{2}w}{{d\varphi }^2}+k^2\cos \varphi \sin \varphi \frac{dw}{d\varphi }+(h-\nu (\nu +1)k^2{\cos }^2\varphi )w=0,$$

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Symbols:

$\cos z$: cosine function, $\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $\sin z$: sine function, $h$: real parameter, $k$: real parameter, $\nu$: real parameter and $\varphi$: change of variable

Permalink:

http://dlmf.nist.gov/29.2.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §29.2(ii), §29.2 and Ch.29

… ►we have …For the Weierstrass function $\mathrm{\wp }$ see §23.2(ii). …

36: Bibliography M

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Crossing symmetric expansions of physical scattering amplitudes: The $O(2,1)$ group and Lamé functions. J. Mathematical Phys. 12, pp. 281–293.

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External Links:

Document, MathReview

Referenced by:

§29.19(ii).

Encodings:

BibTeX

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Die Laméschen Wellenfunktionen des Drehellipsoids. Forschungsbericht No. 1952 ZWB (German).

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Notes:

English translation: Lamé wave functions of the ellipsoid of revolution appeared as NACA Technical Memorandum No. 1224, 1949

External Links:

MathReview

Referenced by:

§30.9(iii).

Encodings:

BibTeX

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37: Bibliography B

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Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems. J. Phys. A 34 (40), pp. 8199–8220.

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External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§29.19(i).

Encodings:

BibTeX

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38: Bibliography L

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Lamé-Wangerin functions. Quart. J. Math., Oxford Ser. (2) 3, pp. 107–114.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§29.17(ii).

Encodings:

BibTeX

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39: Errata

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Over the preceding two months, the subscript parameters of the Ferrers and Legendre functions, ${𝖯}_n,{𝖰}_n,P_n,Q_n,{𝑸}_n$ and the Laguerre polynomial, $L_n$, were incorrectly displayed as superscripts. Reported by Roy Hughes on 2022-05-23

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40: 29.13 Graphics

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Figure 29.13.1: $a_2^m\left(k^2\right)$, $b_2^m\left(k^2\right)$ as functions of $k^2$ for $m=0,1,2$ ($a$’s), $m=1,2$ ($b$’s). Magnify

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Figure 29.13.2: $a_1^m\left(k^2\right)$, $b_1^m\left(k^2\right)$ as functions of $k^2$ for $m=0,1$ ($a$’s), $m=1$ ($b$’s). Magnify

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Figure 29.13.3: $a_3^m\left(k^2\right)$, $b_3^m\left(k^2\right)$ as functions of $k^2$ for $m=0,1,2,3$ ($a$’s), $m=1,2,3$ ($b$’s). Magnify

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Figure 29.13.4: $a_4^m\left(k^2\right)$, $b_4^m\left(k^2\right)$ as functions of $k^2$ for $m=0,1,2,3,4$ ($a$’s), $m=1,2,3,4$ ($b$’s). Magnify

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