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21—30 of 528 matching pages
21: Bibliography J
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Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent.
Phys. D 1 (1), pp. 80–158.
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Asymptotic formulas for the zeros of the Meixner polynomials.
J. Approx. Theory 96 (2), pp. 281–300.
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The Dirichlet boundary value problem for real solutions of the first Painlevé equation on segments in non-positive semi-axis.
J. Reine Angew. Math. 583, pp. 29–86.
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The Painlevé connection problem: An asymptotic approach. I.
Stud. Appl. Math. 86 (4), pp. 315–376.
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Memoire sur l’itération des fonctions rationnelles.
J. Math. Pures Appl. 8 (1), pp. 47–245 (French).
22: Bibliography G
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Basic Hypergeometric Series.
Encyclopedia of Mathematics and its Applications, Vol. 35, Cambridge University Press, Cambridge.
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Basic Hypergeometric Series.
Second edition, Encyclopedia of Mathematics and its Applications, Vol. 96, Cambridge University Press, Cambridge.
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Positive sums of the classical orthogonal polynomials.
SIAM J. Math. Anal. 8 (3), pp. 423–447.
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Algorithm 236: Bessel functions of the first kind.
Comm. ACM 7 (8), pp. 479–480.
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Algorithm 259: Legendre functions for arguments larger than one.
Comm. ACM 8 (8), pp. 488–492.
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23: Bibliography P
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A new basis for the representation of the rotation group. Lamé and Heun polynomials.
J. Mathematical Phys. 14 (8), pp. 1130–1139.
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Unbiasedness of invariant tests for MANOVA and other multivariate problems.
Ann. Statist. 8 (6), pp. 1326–1341.
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Bounds for ratios of modified Bessel functions.
Integral Transform. Spec. Funct. 9 (4), pp. 293–298.
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On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria.
Comput. J. 9 (4), pp. 404–407.
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Elliptic integrals.
Computers in Physics 4 (1), pp. 92–96.
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24: 10.13 Other Differential Equations
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►In (10.13.9)–(10.13.11) , are any cylinder functions of orders , respectively, and .
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10.13.9
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10.13.10
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10.13.11
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►See also Watson (1944, pp. 95–100).
25: 10.22 Integrals
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►In this subsection and denote cylinder functions(§10.2(ii)) of orders and , respectively, not necessarily distinct.
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10.22.5
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►Sufficient conditions for the validity of (10.22.77) are that when , or that and when ; see Titchmarsh (1986a, Theorem 135, Chapter 8) and Akhiezer (1988, p. 62).
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►For collections of Hankel transforms see Erdélyi et al. (1954b, Chapter 8) and Oberhettinger (1972).
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►Sufficient conditions for the validity of (10.22.79) are that when , or that and when ; see Titchmarsh (1962a, pp. 88–90).
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26: Bibliography L
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On the maxima and minima of Bernoulli polynomials.
Amer. Math. Monthly 47 (8), pp. 533–538.
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A partition function connected with the modulus five.
Duke Math. J. 8 (4), pp. 631–655.
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On the theory of diffraction by an aperture in an infinite plane screen. I.
Phys. Rev. 74 (8), pp. 958–974.
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Monotonicity of the differences of zeros of Bessel functions as a function of order.
Proc. Amer. Math. Soc. 15 (1), pp. 91–96.
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Solutions of the fifth Painlevé equation.
Differ. Uravn. 4 (8), pp. 1413–1420 (Russian).
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27: Bibliography U
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On the equation
.
Acta Arith. 51 (4), pp. 349–368.
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On Kelvin’s ship-wave pattern.
J. Fluid Mech. 8 (3), pp. 418–431.
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Integrals with a large parameter: Legendre functions of large degree and fixed order.
Math. Proc. Cambridge Philos. Soc. 95 (2), pp. 367–380.
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28: 29.7 Asymptotic Expansions
29: 8 Incomplete Gamma and Related
Functions
Chapter 8 Incomplete Gamma and Related Functions
…30: Bibliography K
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A proof of the -Macdonald-Morris conjecture for
.
Mem. Amer. Math. Soc. 108 (516), pp. vi+80.
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Special functions and the Bieberbach conjecture.
Amer. Math. Monthly 95 (8), pp. 689–696.
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The addition formula for Laguerre polynomials.
SIAM J. Math. Anal. 8 (3), pp. 535–540.
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Bessel Functions and their Applications.
Analytical Methods and Special Functions, Vol. 8, Taylor & Francis Ltd., London-New York.
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Some special cases of the generalized hypergeometric function
.
J. Comput. Appl. Math. 78 (1), pp. 79–95.
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