Catalan constant
(0.001 seconds)
31—40 of 438 matching pages
31: 8.14 Integrals
32: 30.16 Methods of Computation
…
►For , , ,
…
►If is large, then we can use the asymptotic expansions referred to in §30.9 to approximate .
…
►If is known, then can be found by summing (30.8.1).
The coefficients are computed as the recessive solution of (30.8.4) (§3.6), and normalized via (30.8.5).
…
►The coefficients calculated in §30.16(ii) can be used to compute , from (30.11.3) as well as the connection coefficients from (30.11.10) and (30.11.11).
…
33: 4.34 Derivatives and Differential Equations
34: 8.13 Zeros
…
►
§8.13(i) -Zeros of
►The function has no real zeros for . … ►§8.13(ii) -Zeros of and
►For information on the distribution and computation of zeros of and in the complex -plane for large values of the positive real parameter see Temme (1995a). ►§8.13(iii) -Zeros of
…35: 30.2 Differential Equations
…
►The equation contains three real parameters , , and .
In applications involving prolate spheroidal coordinates is positive, in applications involving oblate spheroidal coordinates is negative; see §§30.13, 30.14.
…
►With Equation (30.2.1) changes to
…
►If , Equation (30.2.1) is the associated Legendre differential equation; see (14.2.2).
…If , Equation (30.2.4) is satisfied by spherical Bessel functions; see (10.47.1).
36: 30.17 Tables
…
►
•
…
►
•
►
•
►
•
…
Stratton et al. (1956) tabulates quantities closely related to and for , , . Precision is 7S.
Hanish et al. (1970) gives and , , and their first derivatives, for , , . The range of is given by if , or , if . Precision is 18S.
Van Buren et al. (1975) gives , for , , . Precision is 8S.
37: 30.11 Radial Spheroidal Wave Functions
…
►Then solutions of (30.2.1) with and are given by
…Here is defined by (30.8.2) and (30.8.6), and
…
►For fixed , as in the sector (),
…
►
30.11.8
…
►where
…