Hankel expansions
(0.002 seconds)
11—20 of 34 matching pages
11: 10.22 Integrals
…
►For asymptotic expansions of Hankel transforms see Wong (1976, 1977), Frenzen and Wong (1985a) and Galapon and Martinez (2014).
…
12: 10.8 Power Series
…
►When is not an integer the corresponding expansions for , , and are obtained by combining (10.2.2) with (10.2.3), (10.4.7), and (10.4.8).
…
13: Bibliography C
…
►
Numerical integration of related Hankel transforms by quadrature and continued fraction expansion.
Geophysics 48 (12), pp. 1671–1686.
…
14: 10.23 Sums
…
►For collections of sums of series involving Bessel or Hankel functions see Erdélyi et al. (1953b, §7.15), Gradshteyn and Ryzhik (2000, §§8.51–8.53), Hansen (1975), Luke (1969b, §9.4), Prudnikov et al. (1986b, pp. 651–691 and 697–700), and Wheelon (1968, pp. 48–51).
15: 10.43 Integrals
…
►For further properties of the Bickley function, including asymptotic expansions and generalizations, see Amos (1983c, 1989) and Luke (1962, Chapter 8).
…
►For asymptotic expansions of the direct transform (10.43.30) see Wong (1981), and for asymptotic expansions of the inverse transform (10.43.31) see Naylor (1990, 1996).
…
16: 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 or is sufficiently small in absolute value.
…
17: 10.57 Uniform Asymptotic Expansions for Large Order
…
►Asymptotic expansions for , , , , , and as that are uniform with respect to can be obtained from the results given in §§10.20 and 10.41 by use of the definitions (10.47.3)–(10.47.7) and (10.47.9).
…
18: Bibliography J
…
►
Numerical calculation of Bessel, Hankel and Airy functions.
Computer Physics Communications 183 (3), pp. 506–519.
►
A note on sampling expansion for a transform with parabolic cylinder kernel.
Inform. Sci. 26 (2), pp. 155–158.
…
►
Uniform asymptotic expansions for Meixner polynomials.
Constr. Approx. 14 (1), pp. 113–150.
…
►
Fast Hankel transforms.
Geophysical Prospecting 27 (4), pp. 876–901.
…
►
Derivation of Green-type, transitional and uniform asymptotic expansions from differential equations. V. Angular oblate spheroidal wavefunctions and for large
.
Proc. Roy. Soc. London Ser. A 321, pp. 545–555.
…
19: 10.21 Zeros
…
►
Zeros of , , ,
… ►The first set of zeros of the principal value of is an infinite string with asymptote , where … ►The zeros of have a similar pattern to those of . The zeros of and are the complex conjugates of the zeros of and , respectively. … ► …20: Bibliography F
…
►
Numerical calculation of singular integrals related to Hankel transform.
Comput. Math. Appl. 21 (2-3), pp. 87–94.
…
►
Expansions of hypergeometric functions in hypergeometric functions.
Math. Comp. 15 (76), pp. 390–395.
…
►
A note on asymptotic evaluation of some Hankel transforms.
Math. Comp. 45 (172), pp. 537–548.
…
►
On the asymptotic expansion of Mellin transforms.
SIAM J. Math. Anal. 18 (1), pp. 273–282.
…
►
Series expansions of symmetric elliptic integrals.
Math. Comp. 81 (278), pp. 957–990.
…