About the Project

Poisson integral

AdvancedHelp

(0.003 seconds)

1—10 of 15 matching pages

1: 1.15 Summability Methods
Poisson Kernel
is the Poisson integral of f ( t ) . … is the conjugate Poisson integral of f ( x ) . … …
2: 1.9 Calculus of a Complex Variable
Poisson Integral
3: 10.9 Integral Representations
Poisson’s and Related Integrals
4: 19.18 Derivatives and Differential Equations
The next four differential equations apply to the complete case of R F and R G in the form R a ( 1 2 , 1 2 ; z 1 , z 2 ) (see (19.16.20) and (19.16.23)). The function w = R a ( 1 2 , 1 2 ; x + y , x y ) satisfies an Euler–Poisson–Darboux equation: …
5: Bibliography K
  • G. A. Kalugin, D. J. Jeffrey, and R. M. Corless (2012) Bernstein, Pick, Poisson and related integral expressions for Lambert W . Integral Transforms Spec. Funct. 23 (11), pp. 817–829.
  • S. H. Khamis (1965) Tables of the Incomplete Gamma Function Ratio: The Chi-square Integral, the Poisson Distribution. Justus von Liebig Verlag, Darmstadt (German, English).
  • 6: Bibliography H
  • L. Habsieger (1988) Une q -intégrale de Selberg et Askey. SIAM J. Math. Anal. 19 (6), pp. 1475–1489.
  • P. I. Hadži (1975a) Certain integrals that contain a probability function. Bul. Akad. Štiince RSS Moldoven. 1975 (2), pp. 86–88, 95 (Russian).
  • H. Hancock (1958) Elliptic Integrals. Dover Publications Inc., New York.
  • T. H. Hildebrandt (1938) Definitions of Stieltjes Integrals of the Riemann Type. Amer. Math. Monthly 45 (5), pp. 265–278.
  • M. Hoyles, S. Kuyucak, and S. Chung (1998) Solutions of Poisson’s equation in channel-like geometries. Comput. Phys. Comm. 115 (1), pp. 45–68.
  • 7: 1.14 Integral Transforms
    §1.14 Integral Transforms
    where the last integral denotes the Cauchy principal value (1.4.25). …
    Poisson’s Summation Formula
    §1.14(viii) Compendia
    For more extensive tables of the integral transforms of this section and tables of other integral transforms, see Erdélyi et al. (1954a, b), Gradshteyn and Ryzhik (2000), Marichev (1983), Oberhettinger (1972, 1974, 1990), Oberhettinger and Badii (1973), Oberhettinger and Higgins (1961), Prudnikov et al. (1986a, b, 1990, 1992a, 1992b).
    8: 1.8 Fourier Series
    (1.8.10) continues to apply if either a or b or both are infinite and/or f ( x ) has finitely many singularities in ( a , b ) , provided that the integral converges uniformly (§1.5(iv)) at a , b , and the singularities for all sufficiently large λ . …
    §1.8(iv) Poisson’s Summation Formula
    It follows from definition (1.14.1) that the integral in (1.8.14) is equal to 2 π ( f ) ( 2 π n ) . …
    1.8.15 1 2 f ( 0 ) + n = 1 f ( n ) = 0 f ( x ) d x + 2 n = 1 0 f ( x ) cos ( 2 π n x ) d x .
    1.8.16 n = e ( n + x ) 2 ω = π ω ( 1 + 2 n = 1 e n 2 π 2 / ω cos ( 2 n π x ) ) , ω > 0 .
    9: Bibliography B
  • G. E. Barr (1968) A note on integrals involving parabolic cylinder functions. SIAM J. Appl. Math. 16 (1), pp. 71–74.
  • W. Bartky (1938) Numerical calculation of a generalized complete elliptic integral. Rev. Mod. Phys. 10, pp. 264–269.
  • P. A. Becker (1997) Normalization integrals of orthogonal Heun functions. J. Math. Phys. 38 (7), pp. 3692–3699.
  • B. C. Berndt (1975a) Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications. J. Number Theory 7 (4), pp. 413–445.
  • P. J. Bushell (1987) On a generalization of Barton’s integral and related integrals of complete elliptic integrals. Math. Proc. Cambridge Philos. Soc. 101 (1), pp. 1–5.
  • 10: 3.5 Quadrature
    See also Poisson’s summation formula (§1.8(iv)). …
    §3.5(vii) Oscillatory Integrals
    Integrals of the form … For the Bromwich integral