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11: Bibliography
  • D. E. Amos, S. L. Daniel, and M. K. Weston (1977) Algorithm 511: CDC 6600 subroutines IBESS and JBESS for Bessel functions I ν ( x ) and J ν ( x ) , x 0 , ν 0 . ACM Trans. Math. Software 3 (1), pp. 93–95.
  • G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen (1992a) Functional inequalities for hypergeometric functions and complete elliptic integrals. SIAM J. Math. Anal. 23 (2), pp. 512–524.
  • G. E. Andrews (1972) Summations and transformations for basic Appell series. J. London Math. Soc. (2) 4, pp. 618–622.
  • T. M. Apostol and I. Niven (1994) Number Theory. In The New Encyclopaedia Britannica, Vol. 25, pp. 14–37.
  • M. J. Atia, A. Martínez-Finkelshtein, P. Martínez-González, and F. Thabet (2014) Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters. J. Math. Anal. Appl. 416 (1), pp. 52–80.
  • 12: Bibliography D
  • H. Davenport (2000) Multiplicative Number Theory. 3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.
  • K. Dilcher (1987b) Irreducibility of certain generalized Bernoulli polynomials belonging to quadratic residue class characters. J. Number Theory 25 (1), pp. 72–80.
  • B. A. Dubrovin (1981) Theta functions and non-linear equations. Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).
  • T. M. Dunster (1997) Error analysis in a uniform asymptotic expansion for the generalised exponential integral. J. Comput. Appl. Math. 80 (1), pp. 127–161.
  • T. M. Dunster (2001b) Uniform asymptotic expansions for Charlier polynomials. J. Approx. Theory 112 (1), pp. 93–133.
  • 13: 32.2 Differential Equations
    See Fuchs (1907), Painlevé (1906), Gromak et al. (2002, §42); also Manin (1998). …
    14: Bibliography K
  • K. W. J. Kadell (1994) A proof of the q -Macdonald-Morris conjecture for B C n . Mem. Amer. Math. Soc. 108 (516), pp. vi+80.
  • E. Kanzieper (2002) Replica field theories, Painlevé transcendents, and exact correlation functions. Phys. Rev. Lett. 89 (25), pp. (250201–1)–(250201–4).
  • E. H. Kaufman and T. D. Lenker (1986) Linear convergence and the bisection algorithm. Amer. Math. Monthly 93 (1), pp. 48–51.
  • A. Kneser (1927) Neue Untersuchungen einer Reihe aus der Theorie der elliptischen Funktionen. Journal für die Reine und Angenwandte Mathematik 158, pp. 209–218 (German).
  • M. Koecher (1954) Zur Theorie der Modulformen n -ten Grades. I. Math. Z. 59, pp. 399–416 (German).
  • 15: Bibliography J
  • M. Jimbo, T. Miwa, Y. Môri, and M. Sato (1980) Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Phys. D 1 (1), pp. 80–158.
  • W. R. Johnson (2007) Atomic Structure Theory: Lectures on Atomic Physics. Springer, Berlin and Heidelberg.
  • D. S. Jones (1964) The Theory of Electromagnetism. International Series of Monographs on Pure and Applied Mathematics, Vol. 47. A Pergamon Press Book, The Macmillan Co., New York.
  • B. R. Judd (1975) Angular Momentum Theory for Diatomic Molecules. Academic Press, New York.
  • B. R. Judd (1976) Modifications of Coulombic interactions by polarizable atoms. Math. Proc. Cambridge Philos. Soc. 80 (3), pp. 535–539.
  • 16: Bibliography P
  • G. Parisi (1988) Statistical Field Theory. Addison-Wesley, Reading, MA.
  • G. Petiau (1955) La Théorie des Fonctions de Bessel Exposée en vue de ses Applications à la Physique Mathématique. Centre National de la Recherche Scientifique, Paris (French).
  • S. Pokorski (1987) Gauge Field Theories. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
  • T. Poston and I. Stewart (1978) Catastrophe Theory and its Applications. Pitman, London.
  • T. Prellberg and A. L. Owczarek (1995) Stacking models of vesicles and compact clusters. J. Statist. Phys. 80 (3–4), pp. 755–779.
  • 17: 22.7 Landen Transformations
    18: Bibliography L
  • L. D. Landau and E. M. Lifshitz (1962) The Classical Theory of Fields. Pergamon Press, Oxford.
  • L. D. Landau and E. M. Lifshitz (1965) Quantum Mechanics: Non-relativistic Theory. Pergamon Press Ltd., Oxford.
  • D. F. Lawden (1989) Elliptic Functions and Applications. Applied Mathematical Sciences, Vol. 80, Springer-Verlag, New York.
  • A. M. Legendre (1808) Essai sur la Théorie des Nombres. 2nd edition, Courcier, Paris.
  • M. Lerch (1903) Zur Theorie der Gaußschen Summen. Math. Ann. 57 (4), pp. 554–567 (German).
  • 19: 10.31 Power Series
    20: Bibliography T
  • J. D. Talman (1983) LSFBTR: A subroutine for calculating spherical Bessel transforms. Comput. Phys. Comm. 30 (1), pp. 93–99.
  • E. C. Titchmarsh (1962) The Theory of Functions. 2nd edition, Oxford University Press, Oxford.
  • P. G. Todorov (1984) On the theory of the Bernoulli polynomials and numbers. J. Math. Anal. Appl. 104 (2), pp. 309–350.
  • C. L. Tretkoff and M. D. Tretkoff (1984) Combinatorial Group Theory, Riemann Surfaces and Differential Equations. In Contributions to Group Theory, Contemp. Math., Vol. 33, pp. 467–519.
  • C. Truesdell (1945) On a function which occurs in the theory of the structure of polymers. Ann. of Math. (2) 46, pp. 144–157.