properties%20of%20solutions

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1: Bibliography R

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Congruence properties of partitions. Math. Z. 9 (1-2), pp. 147–153.

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ISSN 0025-5874, ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.14(v).

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Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.). In Collected Papers,

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Referenced by:

§24.7(i).

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On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

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ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

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Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.

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Notes:

arXiv:1812.02196

Referenced by:

§18.40(ii).

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An extremum property of the $n$-dimensional sphere. J. Phys. A 13 (10), pp. L349–L351.

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ISSN 0305-4470, Document, MathReview

Referenced by:

§5.19(iii).

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2: Bibliography D

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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire $Mx+N$ . Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).

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Notes:

Reprinted in Collected works/Oeuvres scientifiques, Vol. I, pp. 309–425, Académie Royale de Belgique, Brussels, 2000.

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MathReview, ZentralBlatt

Referenced by:

§25.10(i), §27.11, §27.2(i).

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Computational properties of three-term recurrence relations for Kummer functions. J. Comput. Appl. Math. 233 (6), pp. 1505–1510.

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ISSN 0377-0427, Document, FullText, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§13.29(iv), §13.29(iv).

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Unification of one-dimensional Fokker-Planck equations beyond hypergeometrics: Factorizer solution method and eigenvalue schemes. Phys. Rev. E (3) 57 (1), pp. 252–275.

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ISSN 1063-651X, Document, MathReview (Victor I. Stepanov), ZentralBlatt

Referenced by:

§31.17(ii).

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Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.

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Notes:

For a numerical error in one of the zeros see Amos (1985).

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ISSN 0025-5718, FullText, MathReview, ZentralBlatt

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2nd item.

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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.

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Notes:

(This reference has several typographical errors.)

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ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§13.21(ii), §13.21(iii), §13.21(iv).

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3: Bibliography O

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Hyperasymptotic solutions of second-order linear differential equations. I. Methods Appl. Anal. 2 (2), pp. 173–197.

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ISSN 1073-2772, FullText, MathReview (A. D. Wood), ZentralBlatt

Referenced by:

§10.17(v), §10.40(iv), §13.29(i), §13.7(iii), §2.11(v), §9.7(v).

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On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function. Methods Appl. Anal. 5 (4), pp. 425–438.

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ISSN 1073-2772, Pdf, MathReview (Éric Delabaere), ZentralBlatt

Referenced by:

§8.12.

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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series. J. Inst. Math. Appl. 20 (3), pp. 379–391.

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Document, MathReview (David L. Elliott), ZentralBlatt

Referenced by:

§3.11(ii).

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Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.

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ISSN 1615-3375, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§32.17, §32.17.

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Solution of Equations in Euclidean and Banach Spaces. Pure and Applied Mathematics, Vol. 9, Academic Press, New York-London.

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Notes:

Third edition of Solution of equations and systems of equations

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MathReview (J. Burlak), ZentralBlatt

Referenced by:

§3.3(v), §3.8(iii).

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4: 12.10 Uniform Asymptotic Expansions for Large Parameter

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$${𝖠}_1(\tau )=-\frac{1}{12}\tau (20{\tau }^2+30\tau +9),$$

… ►The modified expansion (12.10.31) shares the property of (12.10.3) that it applies when $\mu \to \mathrm{\infty }$ uniformly with respect to $t\in [1+\delta ,\mathrm{\infty })$. In addition, it enjoys a double asymptotic property: it holds if either or both $\mu$ and $t$ tend to infinity. …The proof of the double asymptotic property then follows with the aid of error bounds; compare §10.41(iv). …

5: Bibliography S

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A property of the zeros of cross-product Bessel functions of different orders. Z. Angew. Math. Mech. 56 (2), pp. 120–121.

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Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§10.21(x).

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Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

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Some properties of polynomial sets of type zero. Duke Math. J. 5, pp. 590–622.

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ISSN 0012-7094, Link, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§18.2(xii).

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Staudt and arithmetical properties of Bernoulli numbers. Historia Sci. (2) 5 (1), pp. 69–74.

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ISSN 0285-4821, MathReview (Peter M. Neumann), ZentralBlatt

Referenced by:

§24.10(ii).

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Some combinatorial properties of Jack symmetric functions. Adv. Math. 77 (1), pp. 76–115.

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ISSN 0001-8708, Document, MathReview (Dennis White), ZentralBlatt

Referenced by:

§18.37(iii).

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6: Bibliography N

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§19.37(iv).

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The resurgence properties of the large order asymptotics of the Anger-Weber function I. J. Class. Anal. 4 (1), pp. 1–39.

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ISSN 1848-5979, Document, Link, MathReview (José Luis López), ZentralBlatt

Referenced by:

(11.11.10), (11.11.8), §11.11(iii).

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The resurgence properties of the large order asymptotics of the Anger-Weber function II. J. Class. Anal. 4 (2), pp. 121–147.

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External Links:

ISSN 1848-5979, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

(11.11.10), (11.11.8), §11.11(iii).

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The resurgence properties of the incomplete gamma function II. Stud. Appl. Math. 135 (1), pp. 86–116.

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ISSN 0022-2526, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.11(iii).

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The resurgence properties of the incomplete gamma function, I. Anal. Appl. (Singap.) 14 (5), pp. 631–677.

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ISSN 0219-5305, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.11(iii), §8.11(v), §8.11(v), Erratum (V1.0.14) for Subsections 8.18(ii)–8.11(v).

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7: Bibliography G

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Generalized Functions. Vol. 1: Properties and Operations. Academic Press, New York.

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Notes:

Translated from the Russian by Eugene Saletan. A paperbound reprinting by the same publisher appeared in 1977

External Links:

MathReview, ZentralBlatt

Referenced by:

§2.6(i).

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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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Generalized Fermi-Dirac functions and derivatives: Properties and evaluation. Comput. Phys. Comm. 136 (3), pp. 294–309.

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Notes:

Double-precision Fortran, maximum accuracy 20D

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Document, Code, ZentralBlatt

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7th item.

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Do integrable mappings have the Painlevé property?. Phys. Rev. Lett. 67 (14), pp. 1825–1828.

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ISSN 0031-9007, Document, MathReview, ZentralBlatt

Referenced by:

§32.16.

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A monotonicity property of the power function of multivariate tests. Indag. Math. (N.S.) 11 (2), pp. 209–218.

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ISSN 0019-3577, Document, MathReview (Sumitra Purkayastha), ZentralBlatt

Referenced by:

§35.9.

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8: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:

Document

Referenced by:

§33.22(iv).

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

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Document, Code

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1st item, 4th item.

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

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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

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Integrable Hamiltonian systems and the Painlevé property. Phys. Rev. A (3) 25 (3), pp. 1257–1264.

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ISSN 0556-2791, Document, MathReview

Referenced by:

§32.16.

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Discrete Cosine and Sine Transforms. General Properties, Fast Algorithms and Integer Approximations. Elsevier/Academic Press, Amsterdam.

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ISBN 978-0-12-373624-6; 0-12-373624-2, MathReview (Gerd Teschke)

Referenced by:

§18.3.

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9: Bibliography L

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Monotonicity properties of zeros of generalized Airy functions. Z. Angew. Math. Phys. 39 (2), pp. 267–271.

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ISSN 0044-2275, Document, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§9.13(i).

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An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.11.

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Monotonicity and convexity properties of zeros of Bessel functions. SIAM J. Math. Anal. 8 (1), pp. 171–178.

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ISSN 1095-7154, Document, MathReview (T. Erber), ZentralBlatt

Referenced by:

§10.21(iv).

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Higher monotonicity properties of certain Sturm-Liouville functions. III. Canad. J. Math. 22, pp. 1238–1265.

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ISSN 0008-414X, MathReview (G. Sansone), ZentralBlatt

Referenced by:

§10.21(ii).

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Higher monotonicity properties of certain Sturm-Liouville functions. IV. Canad. J. Math. 24, pp. 349–368.

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External Links:

ISSN 0008-414X, MathReview (G. Sansone), ZentralBlatt

Referenced by:

§10.21(ii).

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