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We study the densities of uniform random walks in the plane.
The problem of the random walk
K. Pearson · 1905
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The random walk
K. Pearson · 1905
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The problem of the random walk
Lord Rayleigh · 1905
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A local probability problem
J. C. Kluyver · 1906
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A mathematical theory of random migration
K. Pearson · 1906
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Ordinary Differential Equations
Edward L. Ince · 1926
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The Theory of Functions
E. Titchmarsh · 1939
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A Treatise on the Theory of Bessel Functions
G. N. Watson · 1941
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On a conjecture of Karl Pearson
H. E. Fettis · 1963
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On epstein’s zeta-function
Atle Selberg and S. Chowla · 1967
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The Special Functions and Their Approximations
Y. L. Luke · 1969
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Speculations concerning the range of Mahler’s measure
David W. Boyd · 1981
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Transform Analysis of Generalized Functions
O. P. Misra and Jean L. Lavoine · 1986
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The Analysis of Linear Partial Differential Operators I
L. Hörmander · 1989
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A cubic counterpart of Jacobi’s identity and the AGM
J. M. Borwein and P. B. Borwein · 1991
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Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind
J. M. Borwein and I. J. Zucker · 1992
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Some cubic modular identities of ramanujan
J.M. Borwein, P.B. Borwein, and F. Garvan · 1994
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Random Walks and Random Environments
Barry D. Hughes · 1995
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Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity
Jonathan M. Borwein and Peter B. Borwein · 1998
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Elliptic integral evaluations of Bessel moments and applications
D. H. Bailey, J. M. Borwein, D. J. Broadhurst, and M. L. Glasser · 2008
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The evaluation of character Euler double sums
J. M. Borwein, I. J. Zucker, and J. Boersma · 2008
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Zeta Mahler measures
Hirotaka Akatsuka · 2009
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Random walk integrals
Jonathan M. Borwein, Dirk Nuyens, Armin Straub, and James Wan · 2009
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Bessel moments, random walks and Calabi-Yau equations
D. J. Broadhurst · 2009
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Analytic representations for circle-jump moments
R. E. Crandall · 2009
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Analytic Combinatorics
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Estimates for Mahler’s measure of a linear form
F. Rodriguez-Villegas, R. Toledano, and J. D. Vaaler · 2004
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Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations
H. A. Verrill · 2004
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Modular forms on S L 2 ( ℤ ) SL_{2}(\mathbb{Z})
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New F 4 5 {}_{5}F_{4} hypergeometric transformations, three-variable Mahler measures, and formulas for 1 / π 1/\pi
M. D. Rogers · 2009
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Hand-to-hand combat: Experimental mathematics with multi-thousand-digit integrals
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New representations for Apéry-like sequences
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Log-sine evaluations of Mahler measures
Jonathan M. Borwein and Armin Straub · 2011
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Three-step and four-step random walk integrals
Jonathan M. Borwein, Armin Straub, and James Wan · 2011
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