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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: 2.1 Definitions and Elementary Properties
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§2.1(i) Asymptotic and Order Symbols
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2.1.5
in .
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§2.1(ii) Integration and Differentiation
►Integration of asymptotic and order relations is permissible, subject to obvious convergence conditions. …8: 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
… ► ► …9: 36.11 Leading-Order Asymptotics
§36.11 Leading-Order Asymptotics
►With real critical points (36.4.1) ordered so that … ►Asymptotics along Symmetry Lines
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36.11.5
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36.11.7
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10: 25.10 Zeros
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