About the Project
NIST

Bessel transform

AdvancedHelp

(0.002 seconds)

1—10 of 49 matching pages

1: 10.74 Methods of Computation
Spherical Bessel Transform
The spherical Bessel transform is the Hankel transform (10.22.76) in the case when ν is half an odd positive integer. …
Kontorovich–Lebedev Transform
2: 10.1 Special Notation
For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
3: Bibliography Z
  • Ya. M. Zhileĭkin and A. B. Kukarkin (1995) A fast Fourier-Bessel transform algorithm. Zh. Vychisl. Mat. i Mat. Fiz. 35 (7), pp. 1128–1133 (Russian).
  • 4: Bibliography L
  • D. Lemoine (1997) Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions. Comput. Phys. Comm. 99 (2-3), pp. 297–306.
  • J. Lund (1985) Bessel transforms and rational extrapolation. Numer. Math. 47 (1), pp. 1–14.
  • 5: Bibliography O
  • F. Oberhettinger (1972) Tables of Bessel Transforms. Springer-Verlag, Berlin-New York.
  • 6: Bibliography T
  • J. D. Talman (1983) LSFBTR: A subroutine for calculating spherical Bessel transforms. Comput. Phys. Comm. 30 (1), pp. 93–99.
  • 7: 10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function
    The Laplace transform of ϕ ( ρ , β ; z ) can be expressed in terms of the Mittag-Leffler function: …
    8: Bibliography S
  • O. A. Sharafeddin, H. F. Bowen, D. J. Kouri, and D. K. Hoffman (1992) Numerical evaluation of spherical Bessel transforms via fast Fourier transforms. J. Comput. Phys. 100 (2), pp. 294–296.
  • A. Sidi (1997) Computation of infinite integrals involving Bessel functions of arbitrary order by the D ¯ -transformation. J. Comput. Appl. Math. 78 (1), pp. 125–130.
  • B. Sommer and J. G. Zabolitzky (1979) On numerical Bessel transformation. Comput. Phys. Comm. 16 (3), pp. 383–387.
  • 9: 13.10 Integrals
    For additional Hankel transforms and also other Bessel transforms see Erdélyi et al. (1954b, §8.18) and Oberhettinger (1972, §§1.16 and 3.4.42–46, 4.4.45–47, 5.94–97). …
    10: 13.23 Integrals
    13.23.6 1 Γ ( 1 + 2 μ ) 2 π i - ( 0 + ) e z t + 1 2 t - 1 t κ M κ , μ ( t - 1 ) d t = z - κ - 1 2 Γ ( 1 2 + μ - κ ) I 2 μ ( 2 z ) , z > 0 .
    13.23.7 1 2 π i - ( 0 + ) e z t + 1 2 t - 1 t κ W κ , μ ( t - 1 ) d t = 2 z - κ - 1 2 Γ ( 1 2 + μ - κ ) Γ ( 1 2 - μ - κ ) K 2 μ ( 2 z ) , z > 0 .
    For additional Hankel transforms and also other Bessel transforms see Erdélyi et al. (1954b, §8.18) and Oberhettinger (1972, §1.16 and 3.4.42–46, 4.4.45–47, 5.94–97). …