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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: Bibliography O
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Hyperasymptotic solutions of second-order linear differential equations. I.
Methods Appl. Anal. 2 (2), pp. 173–197.
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On the calculation of Stokes multipliers for linear differential equations of the second order.
Methods Appl. Anal. 2 (3), pp. 348–367.
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Hyperasymptotic solutions of second-order linear differential equations. II.
Methods Appl. Anal. 2 (2), pp. 198–211.
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Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one.
Proc. Roy. Soc. London Ser. A 454, pp. 1–29.
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Second-order differential equations with fractional transition points.
Trans. Amer. Math. Soc. 226, pp. 227–241.
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5: 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). … … ►6: 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 … ► … ►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 U
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Mathematics of Computation Unpublished Mathematical Tables Collection.
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Integrals with a large parameter: Legendre functions of large degree and fixed order.
Math. Proc. Cambridge Philos. Soc. 95 (2), pp. 367–380.
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9: 10.76 Approximations
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Real Variable and Order Functions
… ►Real Variable and Order Zeros
… ►Real Variable and Order Integrals
… ►Complex Variable; Real Order
… ►Real Variable; Imaginary Order
…10: Frank W. J. Olver
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►Olver joined NIST in 1961 after having been recruited by Milton Abramowitz to be the author of the Chapter “Bessel Functions of Integer Order” in the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, a publication which went on to become the most widely distributed and most highly cited publication in NIST’s history.
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►Most notably, he served as the Editor-in-Chief and Mathematics Editor of the online NIST Digital Library of Mathematical Functions and its 966-page print companion, the NIST Handbook of Mathematical Functions (Cambridge University Press, 2010).
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