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1: Bibliography T

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Special functions in phase space: Mathieu functions. J. Phys. A 31 (31), pp. 6725–6739.

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ISSN 0305-4470, Document, MathReview (Bing Hong Wang), ZentralBlatt

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8th item.

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Sugli zeri delle funzioni di cui si conosce una rappresentazione asintotica. Ann. Mat. Pura Appl. (4) 26, pp. 283–300 (Italian).

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Document, MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§13.9(i).

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Sul comportamento asintotico dell’$n$-esimo polinomio di Laguerre nell’intorno dell’ascissa $4n$ . Comment. Math. Helv. 22, pp. 150–167.

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ISSN 0010-2571, Document, MathReview (G. Szegő), ZentralBlatt

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§18.16(iv).

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Funzioni Ellittiche. 2nd edition, Nicola Zanichelli Editore, Bologna (Italian).

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Notes:

German edition (M. Krafft, Ed.) Akad. Verlag., Leipzig, 1948

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MathReview (Z. Nehari), ZentralBlatt

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Ch.19.

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On a function which occurs in the theory of the structure of polymers. Ann. of Math. (2) 46, pp. 144–157.

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FullText, MathReview (I. Niven), ZentralBlatt

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§25.12(ii), Notations P.

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2: Bibliography Z

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The Dilogarithm Function in Geometry and Number Theory. In Number Theory and Related Topics (Bombay, 1988), R. Askey and others (Eds.), Tata Inst. Fund. Res. Stud. Math., Vol. 12, pp. 231–249.

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MathReview (J. Browkin), ZentralBlatt

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§25.12(i).

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Sul calcolo numerico della funzione di Struve ${𝐇}_{\nu }(z)$ . Rend. Sem. Mat. Univ. e Politec. Torino 32, pp. 251–269 (Italian. English summary).

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MathReview (Walter Gautschi), ZentralBlatt

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§11.13(i), 4th item.

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Integrali di funzioni di Anger, Weber ed Airy-Hardy. Rend. Sem. Mat. Univ. Padova 58, pp. 275–285 (Italian).

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FullText, MathReview (M. E. Muldoon), ZentralBlatt

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§11.10(x).

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Su un integrale definito del prodotto di due funzioni di Struve. Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 112 (1-2), pp. 63–81 (Italian).

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ISSN 0001-4419, MathReview, ZentralBlatt

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§11.7(ii).

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Approximations to -, di- and tri-logarithms. J. Comput. Appl. Math. 202 (2), pp. 450–459.

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ISSN 0377-0427, Document, FullText, MathReview (F. Beukers), ZentralBlatt

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§25.18(i), §25.18(i).

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3: DLMF Project News

error generating summary

4: 32.16 Physical Applications

… ►Statistical physics, especially classical and quantum spin models, has proved to be a major area for research problems in the modern theory of Painlevé transcendents. … ►For applications in 2D quantum gravity and related aspects of the enumerative topology see Di Francesco et al. (1995). For applications in string theory see Seiberg and Shih (2005).

5: Tom M. Apostol

… ► 1923 in Helper, Utah, d. … ►He received his bachelor of science in chemical engineering in 1944 and a master’s degree in mathematics in 1946, both from the University of Washington, Seattle. In 1948, he received his Ph. …In 1950, he arrived at Caltech as an assistant professor; he was named associate professor in 1956, professor in 1962, and professor emeritus in 1992. … ►He was internationally known for his textbooks on calculus, analysis, and analytic number theory, which have been translated into five languages, and for creating Project MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects. …

6: 1.4 Calculus of One Variable

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Faà Di Bruno’s Formula

… ►When the limits in (1.4.22) and (1.4.23) exist, the integrals are said to be convergent. … ►see Rudin (1966), and often used in more abstract mathematical discussions. … ►Delta distributions and Dirac $\delta$-functions are discussed in §§1.16(iii), 1.16(iv) and 1.17. … ►for any $c,d\in (a,b)$, and $t\in [0,1]$. …

7: Bibliography D

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Asymptotic Methods in Analysis. 2nd edition, Bibliotheca Mathematica, Vol. IV, North-Holland Publishing Co., Amsterdam.

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External Links:

MathReview, ZentralBlatt

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§2.2, Ch.2, §26.7(iv), §26.7(iv), §4.13.

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Atomic motions in a rigid sphere gas as a problem in neutron transport. Nucl. Sci. Eng. 24 (2), pp. 142–152.

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§18.39(iii).

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A fast new public code for computing photon orbits in a Kerr spacetime. The Astrophysical Journal 696, pp. 1616–1629.

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Document

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§19.35(ii).

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$2$D gravity and random matrices. Phys. Rep. 254 (1-2), pp. 1–133.

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ISSN 0370-1573, Document, MathReview (Yolanda Lozano)

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§32.16.

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Über die Bestimmung der mittleren Werthe in der Zahlentheorie. Abhandlungen der Königlich Preussischen Akademie der Wissenschaften von 1849, pp. 69–83 (German).

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Reprinted in G. Lejeune Dirichlet’s Werke, Band II, pp. 49–66, Reimer, Berlin, 1897 and with corrections in G. Lejeune Dirichlet’s Werke, AMS Chelsea Publishing Series, Providence, RI, 1969.

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ISBN 0-8284-0225-6, Link, MathReview

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§27.11.

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8: Bibliography G

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Computational Methods in Special Functions – A Survey. In Theory and Application of Special Functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975), R. A. Askey (Ed.), pp. 1–98. Math. Res. Center, Univ. Wisconsin Publ., No. 35.

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MathReview (H. E. Fettis), ZentralBlatt

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§19.36(ii), §19.5.

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Un procedimento di calcolo per le funzioni gamma incomplete. Rend. Sem. Mat. Univ. Politec. Torino 37 (1), pp. 1–9 (Italian).

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MathReview (C. Dagnino), ZentralBlatt

Referenced by:

§3.10(iii).

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Questions of Numerical Condition Related to Polynomials. In Studies in Numerical Analysis, G. H. Golub (Ed.), pp. 140–177.

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MathReview Entry, ZentralBlatt

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§3.8(vi).

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Analysis in homogeneous domains. Uspehi Mat. Nauk 19 (4 (118)), pp. 3–92 (Russian).

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Notes:

In Russian. English translation: Russian Math. Surveys, 19(1964), no. 4, pp. 1–89

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Document, MathReview (A. Korányi), ZentralBlatt

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§35.3(i).

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Error bounds in equilibrium statistical mechanics. J. Math. Phys. 9, pp. 655–663.

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ZentralBlatt

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§18.39(iii), §18.40(ii).

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9: Bibliography

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On the intensity of light in the neighbourhood of a caustic. Trans. Camb. Phil. Soc. 6, pp. 379–402.

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§9.16, §9.16.

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The classical moment problem and some related questions in analysis. Classics in Applied Mathematics, Vol. 82, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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Reprint of the 1965 edition [ 0184042], Translated by N. Kemmer, With a foreword by H. J. Landau

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ISBN 978-1-611976-38-0, MathReview Entry

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§18.40(ii).

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$q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra. CBMS Regional Conference Series in Mathematics, Vol. 66, Amer. Math. Soc., Providence, RI.

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ISBN 0-8218-0716-1, MathReview (David M. Bressoud), ZentralBlatt

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§17.14, §17.14, §17.16, Ch.17, Profile George E. Andrews.

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Umbral calculus, Bailey chains, and pentagonal number theorems. J. Combin. Theory Ser. A 91 (1-2), pp. 464–475.

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In memory of Gian-Carlo Rota

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ISSN 0097-3165, Document, MathReview (Alessandro Di Bucchianico), ZentralBlatt

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§17.12.

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Modular Functions and Dirichlet Series in Number Theory. 2nd edition, Graduate Texts in Mathematics, Vol. 41, Springer-Verlag, New York.

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ISBN 0-387-97127-0, MathReview, ZentralBlatt

Referenced by:

§17.2(i), §23.10(iv), §23.15(i), §23.17(ii), §23.18, §23.18, §23.19, §23.20(i), §23.20(v), Ch.23, §27.14(iii), §27.14(iv), §27.14(vi), §27.7, Ch.27.

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10: Bernard Deconinck

… ► 1970 in Oudenaarde, Belgium) is a Full Professor in the Department of Applied Mathematics at the University of Washington. He received his Diploma in Engineering Physics from the University of Ghent, Belgium. …in Applied Mathematics from the University of Colorado at Boulder, under the direction of Harvey Segur. In addition, he has spent time at the University of Alberta, the Mathematical Sciences Research Institute in Berkeley, California, and Colorado State University. ►Deconinck is interested in nonlinear waves. …