boundary-value%20methods%20or%20problems

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1: Bibliography K

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

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2: Bibliography B

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Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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Document, ZentralBlatt

Referenced by:

§10.73(iv).

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3: Bibliography

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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics. Comput. Phys. Comm. 150 (1), pp. 1–20.

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Notes:

Includes algorithms for Lerch’s transcendent. C and Mathematica codes by Aksenov and Jentschura are available.

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Code, Document

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1st item.

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4: Bibliography G

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Quasirandom distributed bases for bound problems. J. Chem. Phys. 114 (9), pp. 3929–3939.

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Referenced by:

§18.39(iii).

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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.

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FullText, MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§35.2, §35.3(ii).

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Problem 72-21, Laplace transforms of Airy functions. SIAM Rev. 15 (4), pp. 796–798.

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Problem proposed by P. Smith.

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Document

Referenced by:

(9.10.14), (9.10.15), (9.10.16), §9.10(v).

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

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ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, §10.77(ix).

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Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.

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FullText, MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§26.1, §26.1, Notations S, Notations S.

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5: 3.8 Nonlinear Equations

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Bisection Method

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Secant Method

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Eigenvalue Methods

… ►The method converges locally and quadratically, except when the wanted quadratic factor is a multiple factor of $q(z)$. … ►

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: 18.39 Applications in the Physical Sciences

… ►The solutions of (18.39.8) are subject to boundary conditions at $a$ and $b$. … ►

The Quantum Coulomb Problem

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The Relativistic Quantum Coulomb Problem

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The Quantum Coulomb Problem: Scattering States

… ►Shizgal (2015) gives a broad overview of techniques and applications of spectral and pseudo-spectral methods to problems arising in theoretical chemistry, chemical kinetics, transport theory, and astrophysics. …

8: Bibliography L

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The two-point connection problem for differential equations of the Heun class. Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).

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In Russian. English translation: Theoret. and Math. Phys. 101(1994), no. 3, pp. 1413–1418 (1995)

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ISSN 0564-6162, Document, MathReview, ZentralBlatt

Referenced by:

§31.18.

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The central two-point connection problem for the Heun class of ODEs. J. Phys. A 31 (18), pp. 4249–4261.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§31.12.

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Problems of Mathematical Physics. Revised, enlarged and corrected English edition; translated and edited by Richard A. Silverman. With a supplement by Edward L. Reiss, Prentice-Hall Inc., Englewood Cliffs, N.J..

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Notes:

Republished as Worked Problems in Applied Mathematics by Dover Publications, New York, 1979

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ISBN 0-486-63730-1, MathReview (J. Mathews), ZentralBlatt

Referenced by:

§10.43(v).

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Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions. Comput. Phys. Comm. 99 (2-3), pp. 297–306.

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Notes:

Single-precision Fortran, maximum accuracy 8S.

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ISSN 0010-4655, Document, Code, ZentralBlatt

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4th item.

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On incomplete Airy functions and their application to diffraction problems. Radio Sci. 4 (10), pp. 959–969.

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ISSN 0048-6604, Document, MathReview (T. Erber)

Referenced by:

§9.14.

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9: 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. ►Reinhardt firmly believes that the Mandelbrot set is a special function, and notes with interest that the natural boundaries of analyticity of many “more normal” special functions are also fractals. … ►

20 Theta Functions

… ►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.

10: 20.11 Generalizations and Analogs

… ►This is Jacobi’s inversion problem of §20.9(ii). … ►Each provides an extension of Jacobi’s inversion problem. …