connection formulas

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21: 13.2 Definitions and Basic Properties

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§13.2(vii) Connection Formulas

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22: 2.11 Remainder Terms; Stokes Phenomenon

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§2.11(ii) Connection Formulas

… ►However, on combining (2.11.6) with the connection formula (8.19.18), with $m=1$, we derive …

23: 9.12 Scorer Functions

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§9.12(v) Connection Formulas

… ►For other phase ranges combine these results with the connection formulas (9.12.11)–(9.12.14) and the asymptotic expansions given in §9.7. …

24: 25.16 Mathematical Applications

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25.16.12 $$H(s,z)+H(z,s)=\zeta \left(s\right)\zeta \left(z\right)+\zeta \left(s+z\right),$$

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Symbols:

$\zeta \left(s\right)$: Riemann zeta function, $H(s,z)$: generalized Euler sums, $s$: complex variable and $z$: complex variable

Keywords:

addition formula, connectionformula

Source:

Apostol and Vu (1984, (11), p. 91)

Permalink:

http://dlmf.nist.gov/25.16.E12

Encodings:

pMML, png, TeX

See also:

Annotations for §25.16(ii), §25.16 and Ch.25

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25: 28.12 Definitions and Basic Properties

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28.12.15 $${\mathrm{se}}_{\nu }(z,q)=-{\mathrm{se}}_{\nu }(-z,q)=-{\mathrm{se}}_{-\nu }(z,q).$$

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Symbols:

${\mathrm{se}}_n(z,q)$: Mathieu function, $q=h^2$: parameter, $z$: complex variable and $\nu$: complex parameter

Permalink:

http://dlmf.nist.gov/28.12.E15

Encodings:

pMML, png, TeX

See also:

Annotations for §28.12(iii), §28.12 and Ch.28

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26: 30.11 Radial Spheroidal Wave Functions

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Connection Formulas

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27: 13.14 Definitions and Basic Properties

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§13.14(vii) Connection Formulas

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28: 12.14 The Function $W(a,x)$

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§12.14(iv) Connection Formula

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29: Bibliography K

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Connection formulae for the first Painlevé transcendent in the complex domain. Lett. Math. Phys. 27 (4), pp. 243–252.

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External Links:

ISSN 0377-9017, Document, MathReview (B. L. J. Braaksma), ZentralBlatt

Referenced by:

§32.11(i), §32.12(i).

Encodings:

BibTeX

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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External Links:

ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

BibTeX

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30: 10.74 Methods of Computation

… ►The power-series expansions given in §§10.2 and 10.8, together with the connection formulas of §10.4, can be used to compute the Bessel and Hankel functions when the argument $x$ or $z$ is sufficiently small in absolute value. …