T. Amdeberhan, V. H. Moll, and C. Vignat, A probabilistic interpretation of a sequence related to Narayana polynomials, Online Journal of Analytic Combinatorics, vol.8, 2013.

D. H. Bailey, J. M. Borwein, D. M. Broadhurst, and L. Glasser, Elliptic integral representation of Bessel moments, J. Phys. A: Math. Theory, vol.41, pp.5203-5231, 2008.

O. Bernardi, A short proof of Rayleigh's Theorem with extensions, The American Mathematical Monthly, vol.120, issue.4, pp.362-364, 2013.

D. Borwein and J. M. Borwein, Some remarkable properties of sinc and related integrals, Ramanujan J, vol.5, pp.73-90, 2001.

J. M. Borwein, D. Nuyens, A. Straub, and J. Wan, Some arithmetic properties of short random walk integrals, The Ramanujan Journal, vol.26, issue.1, pp.109-132, 2011.

J. M. Borwein and A. Straub, Log-sine evaluations of Mahler measures, J. Aust Math. Soc, vol.92, issue.1, pp.15-36, 2012.

J. M. Borwein, A. Straub, and J. Wan, Three-step and four-step random walk integrals. Experimental Mathematics, vol.22, pp.1-14, 2013.

J. M. Borwein, A. Straub, J. Wan, and W. Zudilin, Densities of short uniform random walks (with an appendix by Don Zagier), Canadian Journal of Mathematics, vol.64, issue.5, pp.961-990, 2012.

D. Boyd, D. Lind, F. R. Villegas, and C. Deninger, The many aspects of Mahler's measure. Final report of 2003 Banff workshop, 2003.

D. J. Broadhurst, Bessel moments, random walks and Calabi-Yau equations, 2009.

P. Djakov and B. Mityagin, Asymptotics of instability zones of Hill operators with a two term potential, C. R. Math. Acad. Sci, vol.339, issue.5, pp.351-354, 2004.

H. E. Fettis, On a conjecture of Karl Pearson. Rider Anniversary Volume, pp.39-54, 1963.

R. García-pelayo, Exact solutions for isotropic random flights in odd dimensions, Journal of Mathematical Physics, vol.53, issue.10, p.103504, 2012.

B. D. Hughes, Random Walks and Random Environments, vol.1, 1995.

J. F. Kingman, Random walks with spherical symmetry, Acta Mathematica, vol.109, issue.1, pp.11-53, 1963.

J. C. Kluyver, A local probability problem, Nederl. Acad. Wetensch. Proc, vol.8, pp.341-350, 1906.

C. Koutschan, Advanced Applications of the Holonomic Systems Approach, 2009.

O. I. Marichev, Handbook of Integral Transforms of Higher Transcendental Functions: Theory and Algorithmic Tables, 1983.

F. W. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions, 2010.

K. Pearson, The problem of the random walk, Nature, vol.72, p.294, 1866.

K. Pearson, A mathematical theory of random migration, Drapers Company Research Memoirs, number 3 in Biometric Series, 1906.

L. Rayleigh, On the problem of random vibrations, and of random flights in one, two, or three dimensions, Philosophical Magazine Series, vol.6, issue.220, pp.321-347, 1919.

L. B. Richmond and J. Shallit, Counting abelian squares, The Electronic Journal of Combinatorics, vol.16, 2009.

M. D. Rogers, New 5 F 4 hypergeometric transformations, three-variable Mahler measures, and formulas for 1/?, Ramanujan Journal, vol.18, issue.3, pp.327-340, 2009.

A. Selberg and S. Chowla, On Epstein's zeta-function, J. Reine Angew. Math, vol.227, pp.86-110, 1967.

N. J. Sloane, The On-Line Encyclopedia of Integer Sequences, 2015.

R. P. Stanley, Enumerative Combinatorics, vol.2, 1999.

E. Titchmarsh, The Theory of Functions, 1939.

H. A. Verrill, Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations, 2004.

J. G. Wan, Random walks, elliptic integrals and related constants, 2013.

G. N. Watson, A Treatise on the Theory of Bessel Functions, 1941.

D. Zeilberger, A holonomic systems approach to special function identities, Journal of Computational and Applied Mathematics, vol.32, issue.3, pp.321-368, 1990.

J. M. Borwein,