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relation to modified Bessel functions

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1: 10.39 Relations to Other Functions
Elementary Functions
Parabolic Cylinder Functions
Confluent Hypergeometric Functions
Generalized Hypergeometric Functions and Hypergeometric Function
2: 13.18 Relations to Other Functions
§13.18(iii) Modified Bessel Functions
3: 13.6 Relations to Other Functions
§13.6(iii) Modified Bessel Functions
4: 12.7 Relations to Other Functions
§12.7(iii) Modified Bessel Functions
5: 9.13 Generalized Airy Functions
Swanson and Headley (1967) define independent solutions A n ( z ) and B n ( z ) of (9.13.1) by …
6: 9.6 Relations to Other Functions
§9.6(i) Airy Functions as Bessel Functions, Hankel Functions, and Modified Bessel Functions
§9.6(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions as Airy Functions
9.6.20 H 2 / 3 ( 2 ) ( ζ ) = e 2 π i / 3 H 2 / 3 ( 2 ) ( ζ ) = e π i / 6 ( 3 / z ) ( Ai ( z ) + i Bi ( z ) ) .
7: 18.34 Bessel Polynomials
where 𝗄 n is a modified spherical Bessel function (10.49.9), and …
8: 10.16 Relations to Other Functions
§10.16 Relations to Other Functions
Elementary Functions
Parabolic Cylinder Functions
Confluent Hypergeometric Functions
Generalized Hypergeometric Functions
9: 10.74 Methods of Computation
Similar observations apply to the computation of modified Bessel functions, spherical Bessel functions, and Kelvin functions. …
§10.74(vii) Integrals
Kontorovich–Lebedev Transform
10: Bibliography C
  • J. B. Campbell (1980) On Temme’s algorithm for the modified Bessel function of the third kind. ACM Trans. Math. Software 6 (4), pp. 581–586.
  • R. Cicchetti and A. Faraone (2004) Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics. IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.
  • W. J. Cody (1983) Algorithm 597: Sequence of modified Bessel functions of the first kind. ACM Trans. Math. Software 9 (2), pp. 242–245.
  • W. J. Cody (1991) Performance evaluation of programs related to the real gamma function. ACM Trans. Math. Software 17 (1), pp. 46–54.
  • H. S. Cohl (2010) Derivatives with respect to the degree and order of associated Legendre functions for | z | > 1 using modified Bessel functions. Integral Transforms Spec. Funct. 21 (7-8), pp. 581–588.