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1: Bibliography Z
  • D. Zagier (1989) 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.
  • R. Zanovello (1975) Sul calcolo numerico della funzione di Struve H ν ( z ) . Rend. Sem. Mat. Univ. e Politec. Torino 32, pp. 251–269 (Italian. English summary).
  • R. Zanovello (1977) Integrali di funzioni di Anger, Weber ed Airy-Hardy. Rend. Sem. Mat. Univ. Padova 58, pp. 275–285 (Italian).
  • R. Zanovello (1978) 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).
  • W. Zudilin (2007) Approximations to -, di- and tri-logarithms. J. Comput. Appl. Math. 202 (2), pp. 450–459.
  • 2: 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).
    3: DLMF Project News
    error generating summary
    4: Bibliography T
  • Go. Torres-Vega, J. D. Morales-Guzmán, and A. Zúñiga-Segundo (1998) Special functions in phase space: Mathieu functions. J. Phys. A 31 (31), pp. 6725–6739.
  • J. F. Traub (1964) Iterative Methods for the Solution of Equations. Prentice-Hall Series in Automatic Computation, Prentice-Hall Inc., Englewood Cliffs, N.J..
  • F. G. Tricomi (1947) Sugli zeri delle funzioni di cui si conosce una rappresentazione asintotica. Ann. Mat. Pura Appl. (4) 26, pp. 283–300 (Italian).
  • F. G. Tricomi (1949) Sul comportamento asintotico dell’ n -esimo polinomio di Laguerre nell’intorno dell’ascissa 4 n . Comment. Math. Helv. 22, pp. 150–167.
  • C. Truesdell (1945) On a function which occurs in the theory of the structure of polymers. Ann. of Math. (2) 46, pp. 144–157.
  • 5: 1.4 Calculus of One Variable
    If f ( x ) is continuous at each point c ( a , b ) , then f ( x ) is continuous on the interval ( a , b ) and we write f C ( a , b ) . …
    Faà Di Bruno’s Formula
    When the limits in (1.4.22) and (1.4.23) exist, the integrals are said to be convergent. … If f ( x ) C n + 1 [ a , b ] , then … for any c , d ( a , b ) , and t [ 0 , 1 ] . …
    6: Bibliography D
  • N. G. de Bruijn (1961) Asymptotic Methods in Analysis. 2nd edition, Bibliotheca Mathematica, Vol. IV, North-Holland Publishing Co., Amsterdam.
  • J. Dexter and E. Agol (2009) A fast new public code for computing photon orbits in a Kerr spacetime. The Astrophysical Journal 696, pp. 1616–1629.
  • P. Di Francesco, P. Ginsparg, and J. Zinn-Justin (1995) 2 D gravity and random matrices. Phys. Rep. 254 (1-2), pp. 1–133.
  • P. G. L. Dirichlet (1849) Über die Bestimmung der mittleren Werthe in der Zahlentheorie. Abhandlungen der Königlich Preussischen Akademie der Wissenschaften von 1849, pp. 69–83 (German).
  • A. L. Dixon and W. L. Ferrar (1930) Infinite integrals in the theory of Bessel functions. Quart. J. Math., Oxford Ser. 1 (1), pp. 122–145.
  • 7: Bibliography G
  • W. Gautschi (1975) 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.
  • W. Gautschi (1979c) Un procedimento di calcolo per le funzioni gamma incomplete. Rend. Sem. Mat. Univ. Politec. Torino 37 (1), pp. 1–9 (Italian).
  • W. Gautschi (1984) Questions of Numerical Condition Related to Polynomials. In Studies in Numerical Analysis, G. H. Golub (Ed.), pp. 140–177.
  • S. G. Gindikin (1964) Analysis in homogeneous domains. Uspehi Mat. Nauk 19 (4 (118)), pp. 3–92 (Russian).
  • C. D. Godsil, M. Grötschel, and D. J. A. Welsh (1995) Combinatorics in Statistical Physics. In Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grötschel, and L. Lovász (Eds.), pp. 1925–1954.
  • 8: Bibliography
  • G. B. Airy (1838) On the intensity of light in the neighbourhood of a caustic. Trans. Camb. Phil. Soc. 6, pp. 379–402.
  • G. E. Andrews (1986) 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.
  • G. E. Andrews (2000) Umbral calculus, Bailey chains, and pentagonal number theorems. J. Combin. Theory Ser. A 91 (1-2), pp. 464–475.
  • T. M. Apostol (1990) Modular Functions and Dirichlet Series in Number Theory. 2nd edition, Graduate Texts in Mathematics, Vol. 41, Springer-Verlag, New York.
  • V. I. Arnol’d (1974) Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).
  • 9: Philip J. Davis
     1923 in Lawrence, Mass. … 2018) received an undergraduate degree in mathematics from Harvard College in 1943. During World War II he worked on problems in aerodynamics for the National Advisory Committee for Aeronautics (NACA) at Langley Airforce Base in Hampton, VA. …in mathematics in 1950 under the supervision of Ralph Boas. … This immediately led to discussions among some of the project members about what might be possible, and the discovery that some interactive graphics work had already been done for the NIST Matrix Market, a publicly available repository of test matrices for comparing the effectiveness of numerical linear algebra algorithms. …
    10: Ira Gessel
     1951 in Philadelphia, Pennsylvania) is Professor Emeritus in the Department of Mathematics at Brandeis University in Waltham, Massachusetts. …from the Massachusetts Institute of Technology in 1977. Gessel has published numerous papers in enumerative combinatorics. … In November 2015, Gessel was named Associate Editor of the following DLMF Chapter …