About the Project

expansions in series of spherical Bessel functions

AdvancedHelp

(0.013 seconds)

1—10 of 24 matching pages

1: 30.10 Series and Integrals
2: 6.10 Other Series Expansions
§6.10(ii) Expansions in Series of Spherical Bessel Functions
3: 8.7 Series Expansions
§8.7 Series Expansions
4: 7.6 Series Expansions
§7.6(ii) Expansions in Series of Spherical Bessel Functions
5: 8.21 Generalized Sine and Cosine Integrals
Spherical-Bessel-Function Expansions
6: 6.18 Methods of Computation
For small or moderate values of x and | z | , the expansion in power series6.6) or in series of spherical Bessel functions6.10(ii)) can be used. …
7: 33.9 Expansions in Series of Bessel Functions
§33.9 Expansions in Series of Bessel Functions
§33.9(i) Spherical Bessel Functions
where the function 𝗃 is as in §10.47(ii), a 1 = 0 , a 0 = ( 2 + 1 ) !! C ( η ) , and …
§33.9(ii) Bessel Functions and Modified Bessel Functions
In this subsection the functions J , I , and K are as in §§10.2(ii) and 10.25(ii). …
8: 10.74 Methods of Computation
The power-series expansions given in §§10.2 and 10.8, together with the connection formulas of §10.4, can be used to compute the Bessel and Hankel functions when the argument x or z is sufficiently small in absolute value. … In the case of the spherical Bessel functions the explicit formulas given in §§10.49(i) and 10.49(ii) are terminating cases of the asymptotic expansions given in §§10.17(i) and 10.40(i) for the Bessel functions and modified Bessel functions. …
Fourier–Bessel Expansion
Spherical Bessel Transform
9: 14.15 Uniform Asymptotic Approximations
In other words, the convergent hypergeometric series expansions of 𝖯 ν μ ( ± x ) are also generalized (and uniform) asymptotic expansions as μ , with scale 1 / Γ ( j + 1 + μ ) , j = 0 , 1 , 2 , ; compare §2.1(v). … Here I and K are the modified Bessel functions10.25(ii)). … For the Bessel functions J and Y see §10.2(ii), and for the env functions associated with J and Y see §2.8(iv). … For convergent series expansions see Dunster (2004). … See also Olver (1997b, pp. 311–313) and §18.15(iii) for a generalized asymptotic expansion in terms of elementary functions for Legendre polynomials P n ( cos θ ) as n with θ fixed. …
10: Bibliography V
  • H. Van de Vel (1969) On the series expansion method for computing incomplete elliptic integrals of the first and second kinds. Math. Comp. 23 (105), pp. 61–69.
  • R. S. Varma (1941) An infinite series of Weber’s parabolic cylinder functions. Proc. Benares Math. Soc. (N.S.) 3, pp. 37.
  • A. N. Vavreck and W. Thompson (1984) Some novel infinite series of spherical Bessel functions. Quart. Appl. Math. 42 (3), pp. 321–324.
  • H. Volkmer (1999) Expansions in products of Heine-Stieltjes polynomials. Constr. Approx. 15 (4), pp. 467–480.
  • H. Volkmer (2021) Fourier series representation of Ferrers function 𝖯 .