hypergeometric differential equation
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31—40 of 81 matching pages
31: 13.16 Integral Representations
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13.16.4
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32: 15.6 Integral Representations
33: Bibliography H
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Solving Ordinary Differential Equations. I. Nonstiff Problems.
2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.
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Solving Ordinary Differential Equations. I. Nonstiff Problems.
2nd edition, Springer-Verlag, Berlin.
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Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems.
2nd edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin.
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Differential Equations: A Modern Approach.
Holt, Rinehart and Winston, New York.
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Two Parametric Eigenvalue Problems of Differential Equations.
In Spectral Theory of Differential Operators (Birmingham, AL,
1981),
North-Holland Math. Stud., Vol. 55, pp. 233–241.
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34: Bibliography B
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Transcendental Functions Satisfying Nonhomogeneous Linear Differential Equations.
The Macmillan Co., New York.
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Ordinary differential equations.
Fourth edition, John Wiley & Sons, Inc., New York.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods.
John Wiley & Sons Ltd., Chichester.
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Numerical Methods for Ordinary Differential Equations.
John Wiley & Sons Ltd., Chichester.
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35: Bibliography N
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Confluent hypergeometric equations and related solvable potentials in quantum mechanics.
J. Math. Phys. 41 (12), pp. 7964–7996.
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Uniform Asymptotic Approximations of Solutions of Second-order Linear Differential Equations, with a Coalescing Simple Turning Point and Simple Pole.
Ph.D. Thesis, University of Maryland, College Park, MD.
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A separating surface for the Painlevé differential equation
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J. Math. Anal. Appl. 193 (3), pp. 817–831.
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Hypergeometric functions.
Acta Math. 94, pp. 289–349.
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Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations
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Pergamon Press, Oxford.
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36: Bibliography K
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On the evaluation of the Gauss hypergeometric function.
C. R. Acad. Bulgare Sci. 45 (6), pp. 35–36.
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Asymptotic behavior of the solutions of the Painlevé equation of the first kind.
Differ. Uravn. 24 (10), pp. 1684–1695 (Russian).
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Rational solutions of the fifth Painlevé equation.
Differential Integral Equations 7 (3-4), pp. 967–1000.
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On differential equations for Sobolev-type Laguerre polynomials.
Trans. Amer. Math. Soc. 350 (1), pp. 347–393.
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An algorithm for solving second order linear homogeneous differential equations.
J. Symbolic Comput. 2 (1), pp. 3–43.
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37: 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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§32.10(iv) Fourth Painlevé Equation
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… ►where the fundamental periods and are linearly independent functions satisfying the hypergeometric equation … ►38: 14.32 Methods of Computation
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►Essentially the same comments that are made in §15.19 concerning the computation of hypergeometric functions apply to the functions described in the present chapter.
In particular, for small or moderate values of the parameters and the power-series expansions of the various hypergeometric function representations given in §§14.3(i)–14.3(iii), 14.19(ii), and 14.20(i) can be selected in such a way that convergence is stable, and reasonably rapid, especially when the argument of the functions is real.
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39: Bibliography V
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Modular hypergeometric residue sums of elliptic Selberg integrals.
Lett. Math. Phys. 58 (3), pp. 223–238.
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Transformations of some Gauss hypergeometric functions.
J. Comput. Appl. Math. 178 (1-2), pp. 473–487.
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A note on the asymptotic expansion of generalized hypergeometric functions.
Anal. Appl. (Singap.) 12 (1), pp. 107–115.
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Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials.
J. Comput. Appl. Math. 213 (2), pp. 488–500.
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On the rational solutions of the second Painlevé equation.
Differ. Uravn. 1 (1), pp. 79–81 (Russian).
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40: Bibliography C
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Elementary Differential Equations.
Clarendon Press, Oxford.
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Algorithm 352: Characteristic values and associated solutions of Mathieu’s differential equation.
Comm. ACM 12 (7), pp. 399–407.
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The numerical solution of linear differential equations in Chebyshev series.
Proc. Cambridge Philos. Soc. 53 (1), pp. 134–149.
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Theory of ordinary differential equations.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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The Numerical Treatment of Differential Equations.
3rd edition, Die Grundlehren der Mathematischen Wissenschaften, Vol. 60, Springer, Berlin.
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