Schwarz reflection principle

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31: 28.2 Definitions and Basic Properties

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Change of Sign of $q$

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28.2.37 $${\mathrm{se}}_{2n+2}(z,-q)={(-1)}^n{\mathrm{se}}_{2n+2}(\frac{1}{2}\pi -z,q).$$

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Symbols:

${\mathrm{se}}_n(z,q)$: Mathieu function, $\pi$: the ratio of the circumference of a circle to its diameter, $q=h^2$: parameter, $n$: integer and $z$: complex variable

Permalink:

http://dlmf.nist.gov/28.2.E37

Encodings:

pMML, png, TeX

See also:

Annotations for §28.2(vi), §28.2 and Ch.28

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32: Bibliography D

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Monodromy of certain Painlevé-VI transcendents and reflection groups. Invent. Math. 141 (1), pp. 55–147.

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External Links:

ISSN 0020-9910, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.9(iii).

Encodings:

BibTeX

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Differential-difference operators associated to reflection groups. Trans. Amer. Math. Soc. 311 (1), pp. 167–183.

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External Links:

ISSN 0002-9947, Link, MathReview (W. A. Al-Salam), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX

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33: 28.4 Fourier Series

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§28.4(v) Change of Sign of $q$

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34: 28.31 Equations of Whittaker–Hill and Ince

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$${\mathrm{ℎ𝑠}}_{2n+2}^{2m+2}(z,-\xi )={(-1)}^m{\mathrm{ℎ𝑠}}_{2n+2}^{2m+2}(\frac{1}{2}\pi -z,\xi ).$$

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35: 18.39 Applications in the Physical Sciences

… ►which is the quantum superposition principle. … … ►where $n$ is now the Bohr Principle Quantum Number. …

36: Bibliography L

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The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity. Methuen and Co., Ltd., London.

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Notes:

Translated from Das Relativitätsprinzip by W. Perrett and G. B. Jeffery. Reprinted by Dover Publications Inc., New York, 1952.

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.6(ii).

Encodings:

BibTeX

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37: 3.6 Linear Difference Equations

… ►Similar principles apply to equation (3.6.1) when $a_n{c}_n\ne 0$, $\forall n$, and $d_n\ne 0$ for some, or all, values of $n$. …

38: 3.1 Arithmetics and Error Measures

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39: 23.20 Mathematical Applications

… ►The addition law states that to find the sum of two points, take the third intersection with $C$ of the chord joining them (or the tangent if they coincide); then its reflection in the $x$-axis gives the required sum. …

40: 36.5 Stokes Sets

… ►One of the sheets is symmetrical under reflection in the plane $y=0$, and is given by …