asymptotic%20approximations
(0.003 seconds)
11—20 of 26 matching pages
11: Bibliography D
…
βΊ
Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
…
βΊ
Uniform asymptotic approximation of Mathieu functions.
Methods Appl. Anal. 1 (2), pp. 143–168.
…
βΊ
Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions.
Methods Appl. Anal. 6 (3), pp. 21–56.
…
βΊ
Uniform asymptotic approximations for the Whittaker functions and
.
Anal. Appl. (Singap.) 1 (2), pp. 199–212.
…
βΊ
Uniform asymptotic approximations for incomplete Riemann zeta functions.
J. Comput. Appl. Math. 190 (1-2), pp. 339–353.
…
12: Bibliography
…
βΊ
Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
…
βΊ
Asymptotic expansions of spheroidal wave functions.
J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.
…
βΊ
On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
…
βΊ
Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
…
βΊ
Rational function approximations for Fermi-Dirac integrals.
The Astrophysical Journal Supplement Series 84, pp. 101–108.
…
13: Bibliography N
…
βΊ
On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
…
βΊ
Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
…
βΊ
Uniform Asymptotic Approximations of Solutions of Second-order Linear Differential Equations, with a Coalescing Simple Turning Point and Simple Pole.
Ph.D. Thesis, University of Maryland, College Park, MD.
…
βΊ
Approximations for the Bessel and Struve functions.
Math. Comp. 43 (168), pp. 551–556.
…
βΊ
A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
…
14: Bibliography K
…
βΊ
Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity.
J. Comput. Appl. Math. 205 (1), pp. 186–206.
…
βΊ
Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
…
βΊ
Uniform asymptotic approximations for the Meixner-Sobolev polynomials.
Anal. Appl. (Singap.) 10 (3), pp. 345–361.
βΊ
Exponentially accurate uniform asymptotic approximations for integrals and Bleistein’s method revisited.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 469 (2153), pp. 20130008, 12.
…
βΊ
Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
…
15: 3.8 Nonlinear Equations
…
βΊFor real functions the sequence of approximations to a real zero will always converge (and converge quadratically) if either:
…
βΊInverse linear interpolation (§3.3(v)) is used to obtain the first approximation:
…
βΊInitial approximations to the zeros can often be found from asymptotic or other approximations to , or by application of the phase principle or Rouché’s theorem; see §1.10(iv).
…
βΊConsider and .
We have and .
…
16: 12.11 Zeros
…
βΊ
§12.11(ii) Asymptotic Expansions of Large Zeros
… βΊWhen the zeros are asymptotically given by and , where is a large positive integer and … βΊ§12.11(iii) Asymptotic Expansions for Large Parameter
βΊFor large negative values of the real zeros of , , , and can be approximated by reversion of the Airy-type asymptotic expansions of §§12.10(vii) and 12.10(viii). … βΊ
12.11.9
…
17: Bibliography S
…
βΊ
Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
…
βΊ
Calculator function approximation.
Amer. Math. Monthly 90 (5), pp. 317–325.
…
βΊ
The accuracy of iterated JWBK approximations for Coulomb radial functions.
Comput. Phys. Comm. 32 (2), pp. 115–119.
…
βΊ
Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
…
βΊ
Approximate Calculation of Multiple Integrals.
Prentice-Hall Inc., Englewood Cliffs, N.J..
…
18: Bibliography R
…
βΊ
Rational Chebyshev approximation by Remes’ algorithms.
Numer. Math. 7 (4), pp. 322–330.
…
βΊ
On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
…
βΊ
Remark on Algorithm 498: Airy functions using Chebyshev series approximations.
ACM Trans. Math. Software 7 (3), pp. 404–405.
…
βΊ
Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. I. Plane Couette flow.
Studies in Appl. Math. 53, pp. 91–110.
βΊ
Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. II. The general theory.
Studies in Appl. Math. 53, pp. 217–224.
…
19: 26.13 Permutations: Cycle Notation
…
βΊSee §26.8 for generating functions, recurrence relations, identities, and asymptotic approximations.
…
20: Bibliography W
…
βΊ
Asymptotic approximations for certain - and - symbols.
J. Phys. A 32 (39), pp. 6901–6902.
…
βΊ
Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions.
In Algorithms for Approximation, A. Iske and J. Levesley (Eds.),
pp. 331–348.
…
βΊ
On uniform asymptotic expansion of definite integrals.
J. Approximation Theory 7 (1), pp. 76–86.
…
βΊ
Asymptotic Approximations of Integrals.
Academic Press Inc., Boston-New York.
βΊ
Error bounds for asymptotic approximations of special functions.
Ann. Numer. Math. 2 (1-4), pp. 181–197.
…