Riccati form
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3 matching pages
1: 9.2 Differential Equation
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§9.2(vi) Riccati Form of Differential Equation
…2: 32.10 Special Function Solutions
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►For certain combinations of the parameters, – 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.
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►In the case , the Riccati equation is
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►In the case when in (32.10.15), the Riccati equation is
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►In the case when in (32.10.23), the Riccati equation is
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►If , then the Riccati equation is
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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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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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A closed form solution of the -wave Bethe-Goldstone equation with an infinite repulsive core.
J. Math. Phys. 27 (4), pp. 1154–1158.
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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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