Stokes multipliers

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1: 2.7 Differential Equations

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$w_2(z)={\mathrm{e}}^{-2\pi \mathrm{i}{\mu }_2}{w}_2(z{\mathrm{e}}^{2\pi \mathrm{i}})+C_2{w}_1(z),$

►in which $C_1$, $C_2$ are constants, the so-called Stokes multipliers. … ►For the calculation of Stokes multipliers see Olde Daalhuis and Olver (1995b). …

2: Bibliography O

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On the calculation of Stokes multipliers for linear differential equations of the second order. Methods Appl. Anal. 2 (3), pp. 348–367.

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External Links:

ISSN 1073-2772, Pdf, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§2.7(ii).

Encodings:

BibTeX

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3: 2.11 Remainder Terms; Stokes Phenomenon

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2.11.20 $$R_n^{(1)}(z)={(-1)}^{n-1}\mathrm{i}{\mathrm{e}}^{({\mu }_2-{\mu }_1)\pi \mathrm{i}}{\mathrm{e}}^{{\lambda }_{2}z}{z}^{{\mu }_2}\left(C_1\sum _{s=0}^{m-1}{(-1)}^s{a}_{s,2}\frac{F_{n+{\mu }_2-{\mu }_1-s}\left(z\right)}{z^s}+R_{m,n}^{(1)}(z)\right),$$

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Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $F_p\left(z\right)$: terminant function, $R_n^{(j)}(z)$: remainder, $a_{s,j}$: coefficients, ${\lambda }_j$: roots, ${\mu }_j$: quantities and $C_1$, $C_2$: Stokes multipliers

Referenced by:

§2.11(v)

Permalink:

http://dlmf.nist.gov/2.11.E20

Encodings:

pMML, png, TeX

See also:

Annotations for §2.11(v), §2.11 and Ch.2

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2.11.21 $$R_n^{(2)}(z)={(-1)}^n\mathrm{i}{\mathrm{e}}^{({\mu }_2-{\mu }_1)\pi \mathrm{i}}{\mathrm{e}}^{{\lambda }_{1}z}{z}^{{\mu }_1}\left(C_2\sum _{s=0}^{m-1}{(-1)}^s{a}_{s,1}\frac{F_{n+{\mu }_1-{\mu }_2-s}\left(z{\mathrm{e}}^{-\pi \mathrm{i}}\right)}{z^s}+R_{m,n}^{(2)}(z)\right),$$

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Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $F_p\left(z\right)$: terminant function, $R_n^{(j)}(z)$: remainder, $a_{s,j}$: coefficients, ${\lambda }_j$: roots, ${\mu }_j$: quantities and $C_1$, $C_2$: Stokes multipliers

Referenced by:

§2.11(v)

Permalink:

http://dlmf.nist.gov/2.11.E21

Encodings:

pMML, png, TeX

See also:

Annotations for §2.11(v), §2.11 and Ch.2

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