Waring%20problem
(0.001 seconds)
1—10 of 184 matching pages
1: 27.13 Functions
…
►
§27.13(iii) Waring’s Problem
►This problem is named after Edward Waring who, in 1770, stated without proof and with limited numerical evidence, that every positive integer is the sum of four squares, of nine cubes, of nineteen fourth powers, and so on. Waring’s problem is to find, for each positive integer , whether there is an integer (depending only on ) such that the equation … ►For example, , , , , , and . … ►The existence of follows from that of because , but only the values and are known exactly. …2: Bibliography H
…
►
Solving Ordinary Differential Equations. I. Nonstiff Problems.
2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.
►
Solving Ordinary Differential Equations. I. Nonstiff Problems.
2nd edition, Springer-Verlag, Berlin.
►
Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems.
2nd edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin.
…
►
Some problems of “Partitio Numerorum” (VI): Further researches in Waring’s Problem.
Math. Z. 23, pp. 1–37.
…
►
A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation.
Arch. Rational Mech. Anal. 73 (1), pp. 31–51.
…
3: Bibliography E
…
►
Waring’s problem.
Amer. Math. Monthly 78 (1), pp. 10–36.
…
4: William P. Reinhardt
…
►Older work on the scattering theory of the atomic Coulomb problem led to the discovery of new classes of orthogonal polynomials relating to the spectral theory of Schrödinger operators, and new uses of old ones: this work was strongly motivated by his original ownership of a 1964 hard copy printing of the original AMS 55 NBS Handbook of Mathematical Functions.
…
►
…
►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
5: 20 Theta Functions
Chapter 20 Theta Functions
…6: 10.73 Physical Applications
…
►Bessel functions first appear in the investigation of a physical problem in Daniel Bernoulli’s analysis of the small oscillations of a uniform heavy flexible chain.
For this problem and its further generalizations, see Korenev (2002, Chapter 4, §37) and Gray et al. (1922, Chapter I, §1, Chapter XVI, §4).
…
►This equation governs problems in acoustic and electromagnetic wave propagation.
…See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25).
…
►More recently, Bessel functions appear in the inverse problem in wave propagation, with applications in medicine, astronomy, and acoustic imaging.
…
7: 29.19 Physical Applications
…
►Simply-periodic Lamé functions ( noninteger) can be used to solve boundary-value problems for Laplace’s equation in elliptical cones.
…
►
§29.19(ii) Lamé Polynomials
… ►Shail (1978) treats applications to solutions of elliptic crack and punch problems. …8: 11.12 Physical Applications
§11.12 Physical Applications
►Applications of Struve functions occur in water-wave and surface-wave problems (Hirata (1975) and Ahmadi and Widnall (1985)), unsteady aerodynamics (Shaw (1985) and Wehausen and Laitone (1960)), distribution of fluid pressure over a vibrating disk (McLachlan (1934)), resistive MHD instability theory (Paris and Sy (1983)), and optical diffraction (Levine and Schwinger (1948)). …9: Bibliography G
…
►
Quasirandom distributed bases for bound problems.
J. Chem. Phys. 114 (9), pp. 3929–3939.
►
The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals.
Ann. of Math. (2) 48 (4), pp. 785–826.
…
►
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.
…
►
Stirling number representation problems.
Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
…
10: 18.40 Methods of Computation
…
►