Bessel equation
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31—40 of 111 matching pages
31: Bibliography D
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Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions.
Proc. Roy. Soc. London Ser. A 440, pp. 37–54.
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Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter.
SIAM J. Math. Anal. 21 (4), pp. 995–1018.
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Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions.
Stud. Appl. Math. 107 (3), pp. 293–323.
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32: 2.8 Differential Equations with a Parameter
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§2.8(iv) Case III: Simple Pole
… ►For other examples of uniform asymptotic approximations and expansions of special functions in terms of Bessel functions or modified Bessel functions of fixed order see §§13.8(iii), 13.21(i), 13.21(iv), 14.15(i), 14.15(iii), 14.20(vii), 15.12(iii), 18.15(i), 18.15(iv), 18.24, 33.20(iv). … ►For further examples of uniform asymptotic approximations in terms of parabolic cylinder functions see §§13.20(iii), 13.20(iv), 14.15(v), 15.12(iii), 18.24. …33: 18.12 Generating Functions
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18.12.2
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34: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►By Bessel’s differential equation in the form (10.13.1) we have the functions (, for see §10.2(ii)) as eigenfunctions with eigenvalue of the self-adjoint extension of the differential operator
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35: 3.6 Linear Difference Equations
§3.6 Linear Difference Equations
… ►§3.6(ii) Homogeneous Equations
… ►§3.6(iv) Inhomogeneous Equations
… ►Example 1. Bessel Functions
►The difference equation …36: 10.38 Derivatives with Respect to Order
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10.38.1
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37: Bibliography B
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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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38: 10.74 Methods of Computation
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►In the case of , the need for initial values can be avoided by application of Olver’s algorithm (§3.6(v)) in conjunction with Equation (10.12.4) used as a normalizing condition, or in the case of noninteger orders, (10.23.15).
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