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Special Functions Bookshelf
Daisuke Kanaizumi edited this page Oct 13, 2019
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- G. Gasper, M. Rahman, Basic Hypergeometric Series, 2nd edition, Encyclopedia of Mathematics and its Applications 96, Cambridge University Press, 2004.
- G. E. Andrews, R. Askey, R. Roy, Special Functions, Encyclopedia of Mathematics and its Applications 96, Cambridge University Press, 1999.
- M. E. H. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable, Encyclopedia of Mathematics and its Applications 98, Cambridge University Press, 2009.
- G. E. Andrews, q-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra, Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics Number 66, American Mathematical Society, 1986.
- R. Koekoek, P. A. Lesky, R. F. Swarttouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues, Springer Monographs in Mathematics, Springer, 2010. (See also: Koornwinder, T. H. (2014). Additions to the formula lists in" Hypergeometric orthogonal polynomials and their q-analogues" by Koekoek, Lesky and Swarttouw. arXiv preprint arXiv:1401.0815.)
- M. Ismail, E. Koelink, Theory and Applications of Special Functions, Springer, 2005.
- Hyperbolic Hypergeometric Functions by Fokko van de Bult
- V. Kac, P. Cheung, Quantum Calculus, Universitext, Springer, 2002.
- T. Ernst, A Comprehensive Treatment of q-Calculus, Birkhauser, 2012.
- The history of q-calculus and a new method, Thomas Ernst, Published 2000.
- Duran, U. (2016). Post quantum calculus (Master thesis, Gaziantep University).
- G. B. Arfken, H. J. Weber, F. E. Harris, Mathematical Methods for Physicists, 7th Edition, Academic Press, 2012.
- E. T. Whittaker, G. N. Watson, A Course of Modern Analysis; an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions (3rd. ed. ) Cambridge University Press, 1920.)
- Olver, F. (1997). Asymptotics and special functions. AK Peters/CRC Press.
- Mathai, A. M., & Haubold, H. J. (2008). Special functions for applied scientists. New York: Springer.
- Nikiforov, A. F., & Uvarov, V. B. (1988). Special functions of mathematical physics. Basel: Birkhäuser.
- Magnus, W., Oberhettinger, F., & Soni, R. P. (2013). Formulas and theorems for the special functions of mathematical physics. Springer Science & Business Media.
- Temme, N. M. (2011). Special functions: An introduction to the classical functions of mathematical physics. John Wiley & Sons.
- G. N. Watson, A Treatise on the Theory of Bessel Functions ( 2nd.ed.) Cambridge University Press, 1966.
- Korenev, B. G. (2002). Bessel functions and their applications. CRC Press.
- Bowman, F. (2012). Introduction to Bessel functions. Courier Corporation.
- Luke, Y. L. (2014). Integrals of Bessel functions. Courier Corporation.
- Askey, R. (1975). Orthogonal polynomials and special functions. SIAM.
- Koekoek, R., & Swarttouw, R. F. (1996). The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. arXiv preprint math/9602214.
- Koelink, E., & Van Assche, W. (Eds.). (2003). Orthogonal polynomials and special functions: Leuven 2002. Springer.
- Walter Gautschi, Orthogonal polynomials: computation and approximation, Oxford University Press, Oxford, 2004.
- Walter Gautschi, Orthogonal polynomials in MATLAB: exercises and solutions, SIAM, Philadelphia, 2016.
- R. Sasaki, Lecture Note: Department of Physics, Kitasato University, November 15,16 2017: Simplest Quantum Mechanics.
- Chan, C. T., Mironov, A., Morozov, A., & Sleptsov, A. (2018). Orthogonal Polynomials in Mathematical Physics. Reviews in Mathematical Physics, 30(06), 1840005.