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21: 4.23 Inverse Trigonometric Functions

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§4.23(iii) Reflection Formulas

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22: 26.9 Integer Partitions: Restricted Number and Part Size

… ►The conjugate partition is obtained by reflecting the Ferrers graph across the main diagonal or, equivalently, by representing each integer by a column of dots. …

23: 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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24: 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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25: 28.4 Fourier Series

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§28.4(v) Change of Sign of $q$

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26: 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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27: 3.1 Arithmetics and Error Measures

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28: 10.11 Analytic Continuation

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29: 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. …

30: 26.6 Other Lattice Path Numbers

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