modified functions
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21—30 of 174 matching pages
21: 28.23 Expansions in Series of Bessel Functions
22: 10.37 Inequalities; Monotonicity
23: 28.34 Methods of Computation
24: 10.72 Mathematical Applications
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§10.72(i) Differential Equations with Turning Points
►Bessel functions and modified Bessel functions are often used as approximants in the construction of uniform asymptotic approximations and expansions for solutions of linear second-order differential equations containing a parameter. … ►If has a double zero , or more generally is a zero of order , , then uniform asymptotic approximations (but not expansions) can be constructed in terms of Bessel functions, or modified Bessel functions, of order . …The order of the approximating Bessel functions, or modified Bessel functions, is , except in the case when has a double pole at . … ►Then for large asymptotic approximations of the solutions can be constructed in terms of Bessel functions, or modified Bessel functions, of variable order (in fact the order depends on and ). …25: 11.7 Integrals and Sums
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§11.7(i) Indefinite Integrals
… ►§11.7(ii) Definite Integrals
… ► ►§11.7(iii) Laplace Transforms
… ►§11.7(v) Compendia
…26: 10.26 Graphics
27: 10.33 Continued Fractions
28: 11.14 Tables
29: 10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function
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10.46.2
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►For incomplete modified Bessel functions and Hankel functions, including applications, see Cicchetti and Faraone (2004).