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1: 28.12 Definitions and Basic Properties
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►Without loss of generality, from now on we replace by .
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§28.12(ii) Eigenfunctions
… ►For , … ► … ►2: 28.2 Definitions and Basic Properties
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►(28.2.1) possesses a fundamental pair of solutions called basic solutions with
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►A solution with the pseudoperiodic property (28.2.14) is called a Floquet
solution with respect to
.
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►The Fourier series of a Floquet solution
…leads to a Floquet solution.
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§28.2(vi) Eigenfunctions
…3: 10.24 Functions of Imaginary Order
§10.24 Functions of Imaginary Order
… ►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). Also, in consequence of (10.24.7)–(10.24.9), when is small either and or and comprise a numerically satisfactory pair depending whether or . … ►4: 10.45 Functions of Imaginary Order
§10.45 Functions of Imaginary Order
… ►The corresponding result for is given by … ►In consequence of (10.45.5)–(10.45.7), and comprise a numerically satisfactory pair of solutions of (10.45.1) when is large, and either and , or and , comprise a numerically satisfactory pair when is small, depending whether or . … ►5: 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
…6: 34.11 Higher-Order Symbols
§34.11 Higher-Order Symbols
…7: 10.77 Software
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§10.77(ii) Bessel Functions–Real Argument and Integer or Half-Integer Order (including Spherical Bessel Functions)
… ►§10.77(iii) Bessel Functions–Real Order and Argument
… ►§10.77(vi) Bessel Functions–Imaginary Order and Real Argument
… ►§10.77(vii) Bessel Functions–Complex Order and Real Argument
… ►§10.77(viii) Bessel Functions–Complex Order and Argument
…8: 10.3 Graphics
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§10.3(i) Real Order and Variable
… ►§10.3(ii) Real Order, Complex Variable
… ►§10.3(iii) Imaginary Order, Real Variable
… ► ►9: 9.15 Mathematical Applications
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►Airy functions play an indispensable role in the construction of uniform asymptotic expansions for contour integrals with coalescing saddle points, and for solutions of linear second-order ordinary differential equations with a simple turning point.
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10: 11.1 Special Notation
§11.1 Special Notation
… ►real variable. | |
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real or complex order. | |
integer order. | |
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