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1: 28.12 Definitions and Basic Properties
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►The introduction to the eigenvalues and the functions of general order proceeds as in §§28.2(i), 28.2(ii), and 28.2(iii), except that we now restrict ; equivalently .
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§28.12(ii) Eigenfunctions
… ►For , … ► … ►2: 28.2 Definitions and Basic Properties
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§28.2(vi) Eigenfunctions
…3: 34.11 Higher-Order Symbols
§34.11 Higher-Order Symbols
…4: 10.24 Functions of Imaginary Order
§10.24 Functions of Imaginary Order
… ►and , are linearly independent solutions of (10.24.1): … ►In consequence of (10.24.6), when is large and comprise a numerically satisfactory pair of solutions of (10.24.1); compare §2.7(iv). … … ►5: 10.45 Functions of Imaginary Order
§10.45 Functions of Imaginary Order
… ►and , are real and linearly independent solutions of (10.45.1): … ►The corresponding result for is given by … ► … ►6: Bibliography L
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Inequalities and approximations for zeros of Bessel functions of small order.
SIAM J. Math. Anal. 14 (2), pp. 383–388.
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On the Darling-Mandelbrot probability density and the zeros of some incomplete gamma functions.
Constr. Approx. 10 (1), pp. 15–30.
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Asymptotic expansions of the Whittaker functions for large order parameter.
Methods Appl. Anal. 6 (2), pp. 249–256.
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Asymptotic expansions of symmetric standard elliptic integrals.
SIAM J. Math. Anal. 31 (4), pp. 754–775.
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Addendum to: “Changing the order of integration”.
J. Austral. Math. Soc. 14, pp. 383–384.
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7: 10.26 Graphics
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§10.26(i) Real Order and Variable
… ►§10.26(ii) Real Order, Complex Variable
… ►§10.26(iii) Imaginary Order, Real Variable
… ► ► …8: Bibliography P
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Smoothing of the Stokes phenomenon for high-order differential equations.
Proc. Roy. Soc. London Ser. A 436, pp. 165–186.
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Exactification of the method of steepest descents: The Bessel functions of large order and argument.
Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.
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A Kummer-type transformation for a hypergeometric function.
J. Comput. Appl. Math. 173 (2), pp. 379–382.
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Zonal Polynomials of Order
Through
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In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (Eds.),
Vol. 2, pp. 199–388.
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Evaluation of the Fermi-Dirac integral of half-integer order.
Zastos. Mat. 21 (2), pp. 289–301.
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9: Bibliography W
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Asymptotic expansions for second-order linear difference equations with a turning point.
Numer. Math. 94 (1), pp. 147–194.
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On the points of inflection of Bessel functions of positive order. II.
Canad. J. Math. 43 (3), pp. 628–651.
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Asymptotic expansions for second-order linear difference equations. II.
Stud. Appl. Math. 87 (4), pp. 289–324.
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Asymptotic expansions for second-order linear difference equations.
J. Comput. Appl. Math. 41 (1-2), pp. 65–94.
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Asymptotic solutions of a fourth order differential equation.
Stud. Appl. Math. 118 (2), pp. 133–152.
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