Kummer-type%20transformations
(0.002 seconds)
21—30 of 244 matching pages
21: 8.26 Tables
…
►
•
…
►
•
…
►
•
…
►
•
Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
22: 23 Weierstrass Elliptic and Modular
Functions
…
23: 2.5 Mellin Transform Methods
§2.5 Mellin Transform Methods
… ►The Mellin transform of is defined by …The inversion formula is given by … ► … ►§2.5(iii) Laplace Transforms with Small Parameters
…24: Bibliography K
…
►
Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
…
►
Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
…
►
Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
…
►
The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
…
►
A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation.
Mir, Moscow.
…
25: 35.2 Laplace Transform
§35.2 Laplace Transform
►Definition
… ►Inversion Formula
… ►Convolution Theorem
►If is the Laplace transform of , , then is the Laplace transform of the convolution , where …26: Bibliography B
…
►
Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
…
►
A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
…
►
Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
…
►
Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
…
►
Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
…
27: Bibliography G
…
►
Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
…
►
Problem 72-21, Laplace transforms of Airy functions.
SIAM Rev. 15 (4), pp. 796–798.
…
►
Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
…
►
Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
…
►
Fourier transforms related to a root system of rank 1.
Transform. Groups 12 (1), pp. 77–116.
…
28: 15.17 Mathematical Applications
…
►The logarithmic derivatives of some hypergeometric functions for which quadratic transformations exist (§15.8(iii)) are solutions of Painlevé equations.
…
►Harmonic analysis can be developed for the Jacobi transform either as a generalization of the Fourier-cosine transform (§1.14(ii)) or as a specialization of a group Fourier transform.
…
►Quadratic transformations give insight into the relation of elliptic integrals to the arithmetic-geometric mean (§19.22(ii)).
…
►By considering, as a group, all analytic transformations of a basis of solutions under analytic continuation around all paths on the Riemann sheet, we obtain the monodromy group.
…
29: 19.15 Advantages of Symmetry
…
►Symmetry in of , , and replaces the five transformations (19.7.2), (19.7.4)–(19.7.7) of Legendre’s integrals; compare (19.25.17).
Symmetry unifies the Landen transformations of §19.8(ii) with the Gauss transformations of §19.8(iii), as indicated following (19.22.22) and (19.36.9).
(19.21.12) unifies the three transformations in §19.7(iii) that change the parameter of Legendre’s third integral.
…
30: 2.11 Remainder Terms; Stokes Phenomenon
…
►