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  • H. Davenport (2000) Multiplicative Number Theory, 3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.
  • B. Davies (1973) Complex zeros of linear combinations of spherical Bessel functions and their derivatives, SIAM J. Math. Anal. 4 (1), pp. 128–133.
  • B. Davies (1984) Integral Transforms and their Applications, 2nd edition, Applied Mathematical Sciences, Vol. 25, Springer-Verlag, New York.
  • H. T. Davis (1933) Tables of Higher Mathematical Functions I, Principia Press, Bloomington, Indiana.
  • H. F. Davis and A. D. Snider (1987) Introduction to Vector Analysis, 5th edition, Allyn and Bacon Inc., Boston, MA.
  • P. J. Davis and P. Rabinowitz (1984) Methods of Numerical Integration, 2nd edition, Computer Science and Applied Mathematics, Academic Press Inc., Orlando, FL.
  • P. J. Davis (1975) Interpolation and Approximation, Dover Publications Inc., New York.
  • S. D. Daymond (1955) The principal frequencies of vibrating systems with elliptic boundaries, Quart. J. Mech. Appl. Math. 8 (3), pp. 361–372.
  • C. de Boor (2001) A Practical Guide to Splines, Revised edition, Applied Mathematical Sciences, Vol. 27, Springer-Verlag, New York.
  • L. de Branges (1985) A proof of the Bieberbach conjecture, Acta Math. 154 (1-2), pp. 137–152.
  • N. G. de Bruijn (1937) Integralen voor de ζ-functie van Riemann, Mathematica (Zutphen) B5, pp. 170–180 (Dutch).
  • N. G. de Bruijn (1961) Asymptotic Methods in Analysis, 2nd edition, Bibliotheca Mathematica, Vol. IV, North-Holland Publishing Co., Amsterdam.
  • N. G. de Bruijn (1981) Pólya’s Theory of Counting, in Applied Combinatorial Mathematics, pp. 144–184.
  • M. G. de Bruin, E. B. Saff and R. S. Varga (1981a) On the zeros of generalized Bessel polynomials. I, Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 1–13.
  • M. G. de Bruin, E. B. Saff and R. S. Varga (1981b) On the zeros of generalized Bessel polynomials. II, Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 14–25.
  • C. de la Vallée Poussin (1896a) Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction ζ(s) de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann, Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
  • C. de la Vallée Poussin (1896b) 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).
  • A. de-Shalit and I. Talmi (1963) Nuclear Shell Theory, Pure and Applied Physics, Vol. 14, Academic Press, New York.
  • P. Dean (1966) The constrained quantum mechanical harmonic oscillator, Proc. Cambridge Philos. Soc. 62, pp. 277–286.
  • S. R. Deans (1983) The Radon Transform and Some of Its Applications, A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.
  • A. Deaño, J. Segura and N. M. Temme (2010) Computational properties of three-term recurrence relations for Kummer functions, J. Comput. Appl. Math. 233 (6), pp. 1505–1510.
  • A. Debosscher (1998) Unification of one-dimensional Fokker-Planck equations beyond hypergeometrics: Factorizer solution method and eigenvalue schemes, Phys. Rev. E (3) 57 (1), pp. 252–275.
  • A. Decarreau, M.-Cl. Dumont-Lepage, P. Maroni, A. Robert and A. Ronveaux (1978a) Formes canoniques des équations confluentes de l’équation de Heun, Ann. Soc. Sci. Bruxelles Sér. I 92 (1-2), pp. 53–78.
  • A. Decarreau, P. Maroni and A. Robert (1978b) Sur les équations confluentes de l’équation de Heun, Ann. Soc. Sci. Bruxelles Sér. I 92 (3), pp. 151–189.
  • B. Deconinck, M. Heil, A. Bobenko, M. van Hoeij and M. Schmies (2004) Computing Riemann theta functions, Math. Comp. 73 (247), pp. 1417–1442.
  • B. Deconinck and J. N. Kutz (2006) Computing spectra of linear operators using the Floquet-Fourier-Hill method, J. Comput. Phys. 219 (1), pp. 296–321.
  • B. Deconinck and H. Segur (1998) The KP equation with quasiperiodic initial data, Phys. D 123 (1-4), pp. 123–152.
  • B. Deconinck and H. Segur (2000) Pole dynamics for elliptic solutions of the Korteweg-de Vries equation, Math. Phys. Anal. Geom. 3 (1), pp. 49–74.
  • B. Deconinck and M. van Hoeij (2001) Computing Riemann matrices of algebraic curves, Phys. D 152/153, pp. 28–46.
  • P. A. Deift and X. Zhou (1995) Asymptotics for the Painlevé II equation, Comm. Pure Appl. Math. 48 (3), pp. 277–337.
  • P. A. Deift (1998) Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics, Vol. 3, New York University Courant Institute of Mathematical Sciences, New York.
  • P. Deift, T. Kriecherbauer, K. T. McLaughlin, S. Venakides and X. Zhou (1999a) Strong asymptotics of orthogonal polynomials with respect to exponential weights, Comm. Pure Appl. Math. 52 (12), pp. 1491–1552.
  • P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides and X. Zhou (1999b) Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Comm. Pure Appl. Math. 52 (11), pp. 1335–1425.
  • L. Dekar, L. Chetouani and T. F. Hammann (1999) Wave function for smooth potential and mass step, Phys. Rev. A 59 (1), pp. 107–112.
  • K. Dekker and J. G. Verwer (1984) Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, CWI Monographs, Vol. 2, North-Holland Publishing Co., Amsterdam.
  • H. Delange (1987) Sur les zéros imaginaires des polynômes de Bernoulli, C. R. Acad. Sci. Paris Sér. I Math. 304 (6), pp. 147–150 (French).
  • H. Delange (1988) On the real roots of Euler polynomials, Monatsh. Math. 106 (2), pp. 115–138.
  • H. Delange (1991) Sur les zéros réels des polynômes de Bernoulli, Ann. Inst. Fourier (Grenoble) 41 (2), pp. 267–309 (French).
  • Delft Numerical Analysis Group (1973) On the computation of Mathieu functions, J. Engrg. Math. 7, pp. 39–61.
  • G. Delic (1979a) Chebyshev expansion of the associated Legendre polynomial PLM(x), Comput. Phys. Comm. 18 (1), pp. 63–71.
  • G. Delic (1979b) Chebyshev series for the spherical Bessel function jl(r), Comput. Phys. Comm. 18 (1), pp. 73–86.
  • P. Deligne, P. Etingof, D. S. Freed, D. Kazhdan, J. W. Morgan and D. R. Morrison (Eds.) (1999) Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2, American Mathematical Society, Providence, RI.
  • M. Deléglise and J. Rivat (1996) Computing π(x): The Meissel, Lehmer, Lagarias, Miller, Odlyzko method, Math. Comp. 65 (213), pp. 235–245.
  • J. Demmel and P. Koev (2006) Accurate and efficient evaluation of Schur and Jack functions, Math. Comp. 75 (253), pp. 223–239.
  • J. B. Dence and T. P. Dence (1999) Elements of the Theory of Numbers, Harcourt/Academic Press, San Diego, CA.
  • Derive (commercial interactive system) Texas Instruments, Inc..
  • R. L. Devaney (1986) An Introduction to Chaotic Dynamical Systems, The Benjamin/Cummings Publishing Co. Inc., Menlo Park, CA.
  • 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.
  • S. C. Dhar (1940) Note on the addition theorem of parabolic cylinder functions, J. Indian Math. Soc. (N. S.) 4, pp. 29–30.
  • P. Di Francesco, P. Ginsparg and J. Zinn-Justin (1995) 2D gravity and random matrices, Phys. Rep. 254 (1-2), pp. 1–133.
  • L. E. Dickson (1919) History of the Theory of Numbers (3 volumes), Carnegie Institution of Washington, Washington, DC.
  • A. R. DiDonato and A. H. Morris (1986) Computation of the incomplete gamma function ratios and their inverses, ACM Trans. Math. Software 12 (4), pp. 377–393.
  • A. R. DiDonato and A. H. Morris (1987) Algorithm 654: Fortran subroutines for computing the incomplete gamma function ratios and their inverses, ACM Trans. Math. Software 13 (3), pp. 318–319.
  • A. R. DiDonato and A. H. Morris (1992) Algorithm 708: Significant digit computation of the incomplete beta function ratios, ACM Trans. Math. Software 18 (3), pp. 360–373.
  • A. R. DiDonato (1978) An approximation for χe-t2/2tpdt, χ>0, p real, Math. Comp. 32 (141), pp. 271–275.
  • P. Dienes (1931) The Taylor Series, Oxford University Press, Oxford.
  • A. Dienstfrey and J. Huang (2006) Integral representations for elliptic functions, J. Math. Anal. Appl. 316 (1), pp. 142–160.
  • K. Dilcher, L. Skula and I. Sh. Slavutskiǐ (1991) Bernoulli Numbers. Bibliography (1713–1990), Queen’s Papers in Pure and Applied Mathematics, Vol. 87, Queen’s University, Kingston, ON.
  • K. Dilcher (1987a) Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials, J. Approx. Theory 49 (4), pp. 321–330.
  • K. Dilcher (1987b) Irreducibility of certain generalized Bernoulli polynomials belonging to quadratic residue class characters, J. Number Theory 25 (1), pp. 72–80.
  • K. Dilcher (1988) Zeros of Bernoulli, generalized Bernoulli and Euler polynomials, Mem. Amer. Math. Soc. 73 (386), pp. iv+94.
  • K. Dilcher (1996) Sums of products of Bernoulli numbers, J. Number Theory 60 (1), pp. 23–41.
  • K. Dilcher (2002) Bernoulli Numbers and Confluent Hypergeometric Functions, in Number Theory for the Millennium, I (Urbana, IL, 2000), pp. 343–363.
  • K. Dilcher (2008) On multiple zeros of Bernoulli polynomials, Acta Arith. 134 (2), pp. 149–155.
  • D. K. Dimitrov and G. P. Nikolov (2010) Sharp bounds for the extreme zeros of classical orthogonal polynomials, J. Approx. Theory 162 (10), pp. 1793–1804.
  • A. M. Din (1981) A simple sum formula for Clebsch-Gordan coefficients, Lett. Math. Phys. 5 (3), pp. 207–211.
  • D. Ding (2000) A simplified algorithm for the second-order sound fields, J. Acoust. Soc. Amer. 108 (6), pp. 2759–2764.
  • H. Ding, K. I. Gross and D. St. P. Richards (1996) Ramanujan’s master theorem for symmetric cones, Pacific J. Math. 175 (2), pp. 447–490.
  • R. B. Dingle (1973) Asymptotic Expansions: Their Derivation and Interpretation, Academic Press, London-New York.
  • P. G. L. Dirichlet (1837) Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält, Abhandlungen der Königlich Preussischen Akademie der Wissenschaften von 1837, pp. 45–81 (German).
  • 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.
  • R. McD. Dodds and G. Wiechers (1972) Vector coupling coefficients as products of prime factors, Comput. Phys. Comm. 4 (2), pp. 268–274.
  • G. Doetsch (1955) Handbuch der Laplace-Transformation. Bd. II. Anwendungen der Laplace-Transformation. 1. Abteilung, Birkhäuser Verlag, Basel und Stuttgart (German).
  • G. C. Donovan, J. S. Geronimo and D. P. Hardin (1999) Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets, SIAM J. Math. Anal. 30 (5), pp. 1029–1056.
  • E. Dorrer (1968) Algorithm 322. F-distribution, Comm. ACM 11 (2), pp. 116–117.
  • J. Dougall (1907) On Vandermonde’s theorem, and some more general expansions, Proc. Edinburgh Math. Soc. 25, pp. 114–132.
  • O. Dragoun and G. Heuser (1971) A program to calculate internal conversion coefficients for all atomic shells without screening, Comput. Phys. Comm. 2 (7), pp. 427–432.
  • P. G. Drazin and R. S. Johnson (1993) Solitons: An Introduction, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge.
  • P. G. Drazin and W. H. Reid (1981) Hydrodynamic Stability, Cambridge University Press, Cambridge.
  • K. Driver and K. Jordaan (2013) Inequalities for extreme zeros of some classical orthogonal and q-orthogonal polynomials, Math. Model. Nat. Phenom. 8 (1), pp. 48–59.
  • C. F. du Toit (1993) Bessel functions Jn(z) and Yn(z) of integer order and complex argument, Comput. Phys. Comm. 78 (1-2), pp. 181–189.
  • B. A. Dubrovin (1981) Theta functions and non-linear equations, Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).
  • B. Dubrovin and M. Mazzocco (2000) Monodromy of certain Painlevé-VI transcendents and reflection groups, Invent. Math. 141 (1), pp. 55–147.
  • J. J. Duistermaat (1974) Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm. Pure Appl. Math. 27, pp. 207–281.
  • D. S. Dummit and R. M. Foote (1999) Abstract Algebra, 2nd edition, Prentice Hall Inc., Englewood Cliffs, NJ.
  • D. Dumont and G. Viennot (1980) A combinatorial interpretation of the Seidel generation of Genocchi numbers, Ann. Discrete Math. 6, pp. 77–87.
  • C. F. Dunkl and Y. Xu (2001) Orthogonal Polynomials of Several Variables, Encyclopedia of Mathematics and its Applications, Vol. 81, Cambridge University Press, Cambridge.
  • B. I. Dunlap and B. R. Judd (1975) Novel identities for simple n-j symbols, J. Mathematical Phys. 16, pp. 318–319.
  • G. V. Dunne and K. Rao (2000) Lamé instantons, J. High Energy Phys..
  • T. M. Dunster, D. A. Lutz and R. Schäfke (1993) Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions, Proc. Roy. Soc. London Ser. A 440, pp. 37–54.
  • T. M. Dunster, R. B. Paris and S. Cang (1998) On the high-order coefficients in the uniform asymptotic expansion for the incomplete gamma function, Methods Appl. Anal. 5 (3), pp. 223–247.
  • T. M. Dunster (1986) Uniform asymptotic expansions for prolate spheroidal functions with large parameters, SIAM J. Math. Anal. 17 (6), pp. 1495–1524.
  • T. M. Dunster (1989) Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions, SIAM J. Math. Anal. 20 (3), pp. 744–760.
  • T. M. Dunster (1990a) Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter, SIAM J. Math. Anal. 21 (4), pp. 995–1018.
  • T. M. Dunster (1990b) Uniform asymptotic solutions of second-order linear differential equations having a double pole with complex exponent and a coalescing turning point, SIAM J. Math. Anal. 21 (6), pp. 1594–1618.
  • T. M. Dunster (1991) Conical functions with one or both parameters large, Proc. Roy. Soc. Edinburgh Sect. A 119 (3-4), pp. 311–327.
  • T. M. Dunster (1992) Uniform asymptotic expansions for oblate spheroidal functions I: Positive separation parameter λ, Proc. Roy. Soc. Edinburgh Sect. A 121 (3-4), pp. 303–320.
  • T. M. Dunster (1994a) Uniform asymptotic approximation of Mathieu functions, Methods Appl. Anal. 1 (2), pp. 143–168.
  • T. M. Dunster (1994b) Uniform asymptotic solutions of second-order linear differential equations having a simple pole and a coalescing turning point in the complex plane, SIAM J. Math. Anal. 25 (2), pp. 322–353.
  • T. M. Dunster (1995) Uniform asymptotic expansions for oblate spheroidal functions II: Negative separation parameter λ, Proc. Roy. Soc. Edinburgh Sect. A 125 (4), pp. 719–737.
  • T. M. Dunster (1996a) Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function, Proc. Roy. Soc. London Ser. A 452, pp. 1331–1349.
  • T. M. Dunster (1996b) Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities, Proc. Roy. Soc. London Ser. A 452, pp. 1351–1367.
  • T. M. Dunster (1996c) Error bounds for exponentially improved asymptotic solutions of ordinary differential equations having irregular singularities of rank one, Methods Appl. Anal. 3 (1), pp. 109–134.
  • 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 (1999) Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions, Methods Appl. Anal. 6 (3), pp. 21–56.
  • T. M. Dunster (2001a) Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions, Stud. Appl. Math. 107 (3), pp. 293–323.
  • T. M. Dunster (2001b) Uniform asymptotic expansions for Charlier polynomials, J. Approx. Theory 112 (1), pp. 93–133.
  • T. M. Dunster (2001c) Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions, SIAM J. Math. Anal. 32 (5), pp. 987–1013.
  • T. M. Dunster (2003a) Uniform asymptotic approximations for the Whittaker functions Mκ,iμ(z) and Wκ,iμ(z), Anal. Appl. (Singap.) 1 (2), pp. 199–212.
  • T. M. Dunster (2003b) Uniform asymptotic expansions for associated Legendre functions of large order, Proc. Roy. Soc. Edinburgh Sect. A 133 (4), pp. 807–827.
  • T. M. Dunster (2004) Convergent expansions for solutions of linear ordinary differential equations having a simple pole, with an application to associated Legendre functions, Stud. Appl. Math. 113 (3), pp. 245–270.
  • T. M. Dunster (2006) Uniform asymptotic approximations for incomplete Riemann zeta functions, J. Comput. Appl. Math. 190 (1-2), pp. 339–353.
  • L. Durand (1975) Nicholson-type Integrals for Products of Gegenbauer Functions and Related Topics, in Theory and Application of Special Functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975), pp. 353–374. Math. Res. Center, Univ. Wisconsin, Publ. No. 35.
  • L. Durand (1978) Product formulas and Nicholson-type integrals for Jacobi functions. I. Summary of results, SIAM J. Math. Anal. 9 (1), pp. 76–86.
  • P. L. Duren (1991) The Legendre Relation for Elliptic Integrals, in Paul Halmos: Celebrating 50 Years of Mathematics, (F. W. Gehring Ed.), pp. 305–315.
  • A. J. Durán and F. A. Grünbaum (2005) A survey on orthogonal matrix polynomials satisfying second order differential equations, J. Comput. Appl. Math. 178 (1-2), pp. 169–190.
  • A. J. Durán (1993) Functions with given moments and weight functions for orthogonal polynomials, Rocky Mountain J. Math. 23, pp. 87–104.
  • J. Dutka (1981) The incomplete beta function—a historical profile, Arch. Hist. Exact Sci. 24 (1), pp. 11–29.
  • A. Dzieciol, S. Yngve and P. O. Fröman (1999) Coulomb wave functions with complex values of the variable and the parameters, J. Math. Phys. 40 (12), pp. 6145–6166.
  • B. Döring (1971) Über die Doppelnullstellen der Ableitung der Besselfunktion, Angewandte Informatik 13, pp. 402–406 (German).
  • B. Döring (1966) Complex zeros of cylinder functions, Math. Comp. 20 (94), pp. 215–222.
  • G. M. D’Ariano, C. Macchiavello and M. G. A. Paris (1994) Detection of the density matrix through optical homodyne tomography without filtered back projection, Phys. Rev. A 50 (5), pp. 4298–4302.
  • M. D’Ocagne (1904) Sur une classe de nombres rationnels réductibles aux nombres de Bernoulli, Bull. Sci. Math. (2) 28, pp. 29–32 (French).