Riccati form

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1: 9.2 Differential Equation

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§9.2(vi) Riccati Form of Differential Equation

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2: 32.10 Special Function Solutions

… ►For certain combinations of the parameters, ${\text{P}}_{\text{II}}$–${\text{P}}_{\text{VI}}$ have particular solutions expressible in terms of the solution of a Riccati differential equation, which can be solved in terms of special functions defined in other chapters. … ►In the case ${\epsilon }_1\alpha +{\epsilon }_2\beta =2$, the Riccati equation is … ►In the case when $n=0$ in (32.10.15), the Riccati equation is … ►In the case when $n=0$ in (32.10.23), the Riccati equation is … ►If $n=1$, then the Riccati equation is …

3: Bibliography O

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Hyperasymptotics for nonlinear ODEs. I. A Riccati equation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2060), pp. 2503–2520.

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External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt

Referenced by:

§2.11(v).

Encodings:

BibTeX

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Hyperasymptotics for nonlinear ODEs. II. The first Painlevé equation and a second-order Riccati equation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2062), pp. 3005–3021.

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External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt

Referenced by:

§2.11(v), §32.12(i).

Encodings:

BibTeX

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A closed form solution of the $s$-wave Bethe-Goldstone equation with an infinite repulsive core. J. Math. Phys. 27 (4), pp. 1154–1158.

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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§30.13(v).

Encodings:

BibTeX

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Algorithm 22: Riccati-Bessel functions of first and second kind. Comm. ACM 3 (11), pp. 600–601.

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Notes:

Includes Algol code, minimum accuracy 9S. For certification see same journal 13(1970), p. 448.

External Links:

ISSN 0001-0782, Document

Referenced by:

§10.77(ii).

Encodings:

BibTeX

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