Bessel and Hankel functions
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11—20 of 66 matching pages
11: 10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function
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►For incomplete modified Bessel functions and Hankel functions, including applications, see Cicchetti and Faraone (2004).
12: 10.19 Asymptotic Expansions for Large Order
§10.19 Asymptotic Expansions for Large Order
►§10.19(i) Asymptotic Forms
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10.19.2
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§10.19(iii) Transition Region
… ►See also §10.20(i).13: 10.6 Recurrence Relations and Derivatives
14: 10.20 Uniform Asymptotic Expansions for Large Order
§10.20 Uniform Asymptotic Expansions for Large Order
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10.20.6
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10.20.9
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§10.20(iii) Double Asymptotic Properties
►For asymptotic properties of the expansions (10.20.4)–(10.20.6) with respect to large values of see §10.41(v).15: 10.7 Limiting Forms
16: 10.3 Graphics
§10.3 Graphics
►§10.3(i) Real Order and Variable
►For the modulus and phase functions , , , and see §10.18. … ►§10.3(ii) Real Order, Complex Variable
… ►§10.3(iii) Imaginary Order, Real Variable
…17: 10.9 Integral Representations
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Mehler–Sonine and Related Integrals
… ►Schläfli–Sommerfeld Integrals
… ►§10.9(iv) Compendia
►For collections of integral representations of Bessel and Hankel functions see Erdélyi et al. (1953b, §§7.3 and 7.12), Erdélyi et al. (1954a, pp. 43–48, 51–60, 99–105, 108–115, 123–124, 272–276, and 356–357), Gröbner and Hofreiter (1950, pp. 189–192), Marichev (1983, pp. 191–192 and 196–210), Magnus et al. (1966, §3.6), and Watson (1944, Chapter 6).18: 10.77 Software
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§10.77(v) Bessel Functions–Real Order and Complex Argument (including Hankel Functions)
…19: 9.17 Methods of Computation
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►In consequence of §9.6(i), algorithms for generating Bessel functions, Hankel functions, and modified Bessel functions (§10.74) can also be applied to , , and their derivatives.
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