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Fourier–Bessel expansion

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11: Bibliography P
  • R. B. Paris (2001a) On the use of Hadamard expansions in hyperasymptotic evaluation. I. Real variables. Proc. Roy. Soc. London Ser. A 457 (2016), pp. 2835–2853.
  • E. Petropoulou (2000) Bounds for ratios of modified Bessel functions. Integral Transform. Spec. Funct. 9 (4), pp. 293–298.
  • R. Piessens (1982) Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.
  • A. Pinkus and S. Zafrany (1997) Fourier Series and Integral Transforms. Cambridge University Press, Cambridge.
  • M. Puoskari (1988) A method for computing Bessel function integrals. J. Comput. Phys. 75 (2), pp. 334–344.
  • 12: 28.23 Expansions in Series of Bessel Functions
    §28.23 Expansions in Series of Bessel Functions
    𝒞 μ ( 1 ) = J μ ,
    𝒞 μ ( 3 ) = H μ ( 1 ) ,
    𝒞 μ ( 4 ) = H μ ( 2 ) ;
    13: Bibliography L
  • M. J. Lighthill (1958) An Introduction to Fourier Analysis and Generalised Functions. Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, New York.
  • J. L. López (2001) Uniform asymptotic expansions of symmetric elliptic integrals. Constr. Approx. 17 (4), pp. 535–559.
  • D. Ludwig (1966) Uniform asymptotic expansions at a caustic. Comm. Pure Appl. Math. 19, pp. 215–250.
  • Y. L. Luke (1959) Expansion of the confluent hypergeometric function in series of Bessel functions. Math. Tables Aids Comput. 13 (68), pp. 261–271.
  • J. N. Lyness (1971) Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature. Math. Comp. 25 (113), pp. 87–104.
  • 14: Bibliography R
  • M. Razaz and J. L. Schonfelder (1980) High precision Chebyshev expansions for Airy functions and their derivatives. Technical report University of Birmingham Computer Centre.
  • I. S. Reed, D. W. Tufts, X. Yu, T. K. Truong, M. T. Shih, and X. Yin (1990) Fourier analysis and signal processing by use of the Möbius inversion formula. IEEE Trans. Acoustics, Speech, Signal Processing 38, pp. 458–470.
  • M. Reed and B. Simon (1975) Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness. Academic Press, New York.
  • F. E. Relton (1965) Applied Bessel Functions. Dover Publications Inc., New York.
  • M. D. Rogers (2005) Partial fractions expansions and identities for products of Bessel functions. J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
  • 15: Bibliography D
  • B. Deconinck and J. N. Kutz (2006) Computing spectra of linear operators using the Floquet-Fourier-Hill method. J. Comput. Phys. 219 (1), pp. 296–321.
  • H. Delange (1991) Sur les zéros réels des polynômes de Bernoulli. Ann. Inst. Fourier (Grenoble) 41 (2), pp. 267–309 (French).
  • T. M. Dunster, D. A. Lutz, and R. Schäfke (1993) Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions. Proc. Roy. Soc. London Ser. A 440, pp. 37–54.
  • T. M. Dunster (2001a) Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Stud. Appl. Math. 107 (3), pp. 293–323.
  • T. M. Dunster (2001c) Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions. SIAM J. Math. Anal. 32 (5), pp. 987–1013.
  • 16: Bibliography T
  • I. C. Tang (1969) Some definite integrals and Fourier series for Jacobian elliptic functions. Z. Angew. Math. Mech. 49, pp. 95–96.
  • N. M. Temme (1990b) Uniform asymptotic expansions of a class of integrals in terms of modified Bessel functions, with application to confluent hypergeometric functions. SIAM J. Math. Anal. 21 (1), pp. 241–261.
  • A. Terras (1999) Fourier Analysis on Finite Groups and Applications. London Mathematical Society Student Texts, Vol. 43, Cambridge University Press, Cambridge.
  • E. C. Titchmarsh (1986a) Introduction to the Theory of Fourier Integrals. Third edition, Chelsea Publishing Co., New York.
  • G. P. Tolstov (1962) Fourier Series. Prentice-Hall Inc., Englewood Cliffs, N.J..
  • 17: Bibliography B
  • C. B. Balogh (1967) Asymptotic expansions of the modified Bessel function of the third kind of imaginary order. SIAM J. Appl. Math. 15, pp. 1315–1323.
  • R. Bo and R. Wong (1994) Uniform asymptotic expansion of Charlier polynomials. Methods Appl. Anal. 1 (3), pp. 294–313.
  • P. Boalch (2005) From Klein to Painlevé via Fourier, Laplace and Jimbo. Proc. London Math. Soc. (3) 90 (1), pp. 167–208.
  • F. Bowman (1958) Introduction to Bessel Functions. Dover Publications Inc., New York.
  • J. Brüning (1984) On the asymptotic expansion of some integrals. Arch. Math. (Basel) 42 (3), pp. 253–259.
  • 18: Bibliography K
  • E. G. Kalnins and W. Miller (1991a) Hypergeometric expansions of Heun polynomials. SIAM J. Math. Anal. 22 (5), pp. 1450–1459.
  • E. G. Kalnins and W. Miller (1991b) Addendum: “Hypergeometric expansions of Heun polynomials”. SIAM J. Math. Anal. 22 (6), pp. 1803.
  • D. Karp, A. Savenkova, and S. M. Sitnik (2007) Series expansions for the third incomplete elliptic integral via partial fraction decompositions. J. Comput. Appl. Math. 207 (2), pp. 331–337.
  • T. W. Körner (1989) Fourier Analysis. 2nd edition, Cambridge University Press, Cambridge.
  • V. I. Krylov and N. S. Skoblya (1985) A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation. Mir, Moscow.
  • 19: 18.17 Integrals
    §18.17(v) Fourier Transforms
    Jacobi
    Ultraspherical
    Legendre
    Hermite
    20: Bibliography H
  • P. I. Hadži (1976a) Expansions for the probability function in series of Čebyšev polynomials and Bessel functions. Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).
  • F. E. Harris (2000) Spherical Bessel expansions of sine, cosine, and exponential integrals. Appl. Numer. Math. 34 (1), pp. 95–98.
  • P. Henrici (1986) Applied and Computational Complex Analysis. Vol. 3: Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons Inc.], New York.
  • C. J. Howls and A. B. Olde Daalhuis (1999) On the resurgence properties of the uniform asymptotic expansion of Bessel functions of large order. Proc. Roy. Soc. London Ser. A 455, pp. 3917–3930.
  • J. Humblet (1985) Bessel function expansions of Coulomb wave functions. J. Math. Phys. 26 (4), pp. 656–659.