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1: Bibliography N

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An extension of Laplace’s method. Constr. Approx. 51 (2), pp. 247–272.

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External Links:

ISSN 0176-4276, Document, Link, MathReview (José Luis López), ZentralBlatt

Referenced by:

(11.11.16), (11.11.17), §11.11(iii).

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Elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 99–102.

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Notes:

Includes Algol program.

External Links:

MathReview

Referenced by:

§19.39(iii).

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On the calculation of elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 91–94.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§19.36(ii).

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Special Functions of Mathematical Physics: A Unified Introduction with Applications. Birkhäuser Verlag, Basel.

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Notes:

Translated from the Russian and with a preface by Ralph P. Boas, with a foreword by A. A. Samarskiĭ

External Links:

ISBN 3-7643-3183-6, MathReview, ZentralBlatt

Referenced by:

§18.18(i), Erratum (V1.2.0) Section 18.39.

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Evaluation of negative energy Coulomb (Whittaker) functions. Comput. Phys. Comm. 159 (1), pp. 55–62.

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Notes:

Double-precision Fortran-90 code.

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Document, Code

Referenced by:

§33.23(vi), 8th item.

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2: Philip J. Davis

… ►in mathematics in 1950 under the supervision of Ralph Boas. …

3: Bibliography M

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On the computation of zeroes of $J_n(z)-i{J}_{n+1}(z)=0$ . Quart. Appl. Math. 55 (4), pp. 623–633.

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External Links:

ISSN 0033-569X, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.21(ix).

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Formulas and Theorems for the Special Functions of Mathematical Physics. 3rd edition, Springer-Verlag, New York-Berlin.

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Notes:

Table errata: Math. Comp. v. 23 (1969), p. 471, v. 24 (1970), pp. 240 and 505, v. 25 (1971), no. 113, p. 201, v. 29 (1975), no. 130, p. 672, v. 30 (1976), no. 135, pp. 677–678, v. 32 (1978), no. 141, pp. 319–320, v. 36 (1981), no. 153, pp. 315–317, v. 41 (1983), no. 164, pp. 775–776, and v. 81 (2012), no. 280, p. 2251

External Links:

MathReview (Mary L. Boas), ZentralBlatt

Referenced by:

§10.15, §10.22(vi), §10.32(iv), §10.38, §10.43(vi), §10.60(iv), §10.9(iv), §11.5(iii), Ch.11, §12.12, §12.5(iv), Ch.12, §13.10(vi), §13.23(iv), §14.1, §14.11, §14.12(ii), §14.18(iv), §14.25, §14.3(iii), §14.5(v), §14.7(iv), Ch.14, (25.5.21), §25.5, (25.6.1), (25.6.2), §25.6(i), §8.1, Notations B, Notations I, Notations P, Notations P, Notations Q, Notations Q.

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Rational solutions of the Painlevé VI equation. J. Phys. A 34 (11), pp. 2281–2294.

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ISSN 0305-4470, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.8(vi).

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Inequalities for the zeros of Bessel functions. SIAM J. Math. Anal. 8 (1), pp. 166–170.

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ISSN 1095-7154, Document, MathReview (Mary L. Boas), ZentralBlatt

Referenced by:

§10.21(iv).

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Analytic Inequalities. Springer-Verlag, New York.

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Notes:

Addenda: Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., no. 634–677 (1979), pp. 3–24 and no. 577-598 (1977), pp. 3–10.

External Links:

MathReview (R. A. Askey and R. P. Boas, Jr.), ZentralBlatt

Referenced by:

§4.18, §4.32, §4.5(i), §4.5(ii), §7.8.

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4: Bibliography C

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New proof of the addition theorem for Gegenbauer polynomials. SIAM J. Math. Anal. 2, pp. 347–351.

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External Links:

ISSN 1095-7154, Document, MathReview (Mary L. Boas), ZentralBlatt

Referenced by:

§18.18(ii).

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Generalized incomplete gamma functions with applications. J. Comput. Appl. Math. 55 (1), pp. 99–124.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.16.

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A numerical method for generalized exponential integrals. Comput. Math. Appl. 14 (4), pp. 261–268.

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External Links:

ISSN 0898-1221, MathReview (R. P. Boas), ZentralBlatt

Referenced by:

§8.25(v).

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Catastrophes and molecular collisions. Molecular Phys. 31 (1), pp. 33–55.

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External Links:

Document, MathReview (V. M. Zakaljukin)

Referenced by:

§36.14(iii).

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$S$-matrix and $R$-matrix determination of the low-energy ${}_{}{}^5\mathrm{He}$ and ${}_{}{}^5\mathrm{Li}$ resonance parameters. Phys. Rev. C 55 (1), pp. 536–539.

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External Links:

Document

Referenced by:

2nd item.

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5: Bibliography T

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Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations. Phys. Rev. Lett. 29 (16), pp. 1114–1118.

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External Links:

Document

Referenced by:

§31.17(ii).

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Fourier Series. Prentice-Hall Inc., Englewood Cliffs, N.J..

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Notes:

Translated from the Russian by Richard A. Silverman. Second English edition published by Dover Publications Inc., New York, 1976.

External Links:

MathReview (R. P. Boas, Jr.), ZentralBlatt

Referenced by:

§1.8(i), §1.8(ii).

Encodings:

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Numerical evaluation of exponential integral: Theis well function approximation. Journal of Hydrology 205 (1-2), pp. 38–51.

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External Links:

Document

Referenced by:

§6.18(i).

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6: Bibliography

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On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations. Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.

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External Links:

ISSN 0024-1318, MathReview (James M. Horner)

Referenced by:

§13.9(i).

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A general mode theory for the elliptic disk microstrip antenna. IEEE Trans. Antennas and Propagation 43 (6), pp. 560–568.

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External Links:

Document

Referenced by:

5th item.

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Table of Definite and Infinite Integrals. Physical Sciences Data, Vol. 13, Elsevier Scientific Publishing Co., Amsterdam.

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Notes:

Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1386.

External Links:

ISBN 0-444-42151-3, MathReview (R. P. Boas), ZentralBlatt

Referenced by:

§1.4(iv), §10.22(vi), §10.43(vi), §11.7(v), §11.9(iv), §12.5(iv), §13.10(vi), §13.23(v), §15.14, §16.20, §16.5, §18.17(ix), §4.10(iii), §4.26(v), §4.40(v), §5.13, §6.14(iii), §7.14(iii), §8.14, §8.19(x).

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Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).

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Notes:

Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ (1901–1973), I. In Russian. English translation: Russian Math. Surveys, 29(1974), no. 2, pp. 10–50.

External Links:

Document, MathReview (G. R. Belickii), ZentralBlatt

Referenced by:

§36.2(i).

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Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Mem. Amer. Math. Soc. 54 (319), pp. iv+55.

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External Links:

ISSN 0065-9266, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§18.21(ii), §18.22(ii), (18.28.24), §18.28(ii), Ch.18, Profile Richard A. Askey.

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7: Bibliography G

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Sur les équations différentielles du second ordre et du premier degré dont l’intégrale générale est a points critiques fixes. Acta Math. 33 (1), pp. 1–55.

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External Links:

ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt

Referenced by:

§32.10(ii), §32.10(iv), §32.7(ii).

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Algorithm 292: Regular Coulomb wave functions. Comm. ACM 9 (11), pp. 793–795.

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External Links:

ISSN 0001-0782, Document

Referenced by:

§33.26(ii).

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

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External Links:

FullText, MathReview (L. Carlitz), ZentralBlatt

Referenced by:

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

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Integraltafel. Erster Teil. Unbestimmte Integrale. Springer-Verlag, Vienna.

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Notes:

Reprintings with corrections appeared in 1961 and 1965

External Links:

MathReview (R. P. Boas, Jr.), ZentralBlatt

Referenced by:

§1.4(iv), §23.14, §4.10(iii), §4.26(v), §4.40(v).

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Theory of Painlevé’s equations. Differ. Uravn. 11 (11), pp. 373–376 (Russian).

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Notes:

In Russian. English translation: Differential Equations 11(11), pp. 285–287

External Links:

MathReview (Z. Nehari), ZentralBlatt

Referenced by:

§32.7(iii), §32.7(vi).

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8: Bibliography L

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Eine Verallgemeinerung der Sphäroidfunktionen. Arch. Math. 11, pp. 29–39.

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ISSN 0003-9268, Document, MathReview (M. J. O. Strutt), ZentralBlatt

Referenced by:

§30.12.

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An application of the finite element approximation method to find the complex zeros of the modified Bessel function $K_n(z)$ . Math. Comp. 33 (148), pp. 1299–1306.

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External Links:

ISSN 0025-5718, FullText, MathReview (R. P. Boas, Jr.), ZentralBlatt

Referenced by:

§10.74(vi), 2nd item.

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Higher monotonicity properties of certain Sturm-Liouville functions.. Acta Math. 109, pp. 55–73.

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External Links:

ISSN 0001-5962, Document, MathReview (G. Sansone), ZentralBlatt

Referenced by:

§10.21(ii).

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Algorithm 244: Fresnel integrals. Comm. ACM 7 (11), pp. 660–661.

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Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

ISSN 0001-0782, Document

Referenced by:

§7.25(iv).

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On the theory of Painlevé’s third equation. Differ. Uravn. 3 (11), pp. 1913–1923 (Russian).

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Notes:

In Russian. English translation: Differential Equations 3(11), pp. 994–999

External Links:

MathReview (Z. Nehari), ZentralBlatt

Referenced by:

§32.10(iii), §32.8(iii), §32.9(i), §32.9(ii).

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9: Bibliography S

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On integral representations for Lamé and other special functions. SIAM J. Math. Anal. 11 (4), pp. 702–723.

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External Links:

ISSN 0036-1410, Document, MathReview (R. K. Gupta), ZentralBlatt

Referenced by:

§29.17(i), §29.8.

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The Laplace transforms of products of Airy functions. Dirāsāt Ser. B Pure Appl. Sci. 19 (2), pp. 7–11.

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External Links:

ISSN 0253-424X, MathReview

Referenced by:

§9.10(v).

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The Problem of Moments. 4th edition, American Mathematical Society Mathematical Surveys, Vol. 1, American Mathematical Society, Providence, RI.

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External Links:

MathReview (R. P. Boas, Jr.), ZentralBlatt

Referenced by:

§1.16(ix), §1.4(v), §18.2(viii), (18.40.7), §18.40(ii), §18.40(ii).

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A simple approach to asymptotic expansions for Fourier integrals of singular functions. Appl. Math. Comput. 216 (11), pp. 3378–3385.

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External Links:

ISSN 0096-3003, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§2.3(iv).

Encodings:

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Représentation asymptotique de la solution générale de l’équation de Mathieu-Hill. Acad. Roy. Belg. Bull. Cl. Sci. (5) 51 (11), pp. 1415–1446.

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External Links:

ZentralBlatt

Referenced by:

§28.8(ii).

Encodings:

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10: 25.20 Approximations

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Cody et al. (1971) gives rational approximations for $\zeta \left(s\right)$ in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are $0.5\le s\le 5$, $5\le s\le 11$, $11\le s\le 25$, $25\le s\le 55$. Precision is varied, with a maximum of 20S.

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