Math Surveys

I used arXiv Vanity to convert arXiv PDF files to HTML.

• An introduction to Ramanujan's “lost” notebook, GE Andrews - The American Mathematical Monthly, 1979.
• The history of q-calculus and a new method, Thomas Ernst, Published 2000.

Special Functions

Orthogonal Polynomials

• Koekoek, R., & Swarttouw, R. F. (1996). The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. arXiv preprint math/9602214.
• Gautschi, W. (1996). Orthogonal polynomials: applications and computation. Acta Numerica, 5, 45-119.
• Diekema, E., & Koornwinder, T. H. (2012). Differentiation by integration using orthogonal polynomials, a survey. Journal of Approximation Theory, 164(5), 637-667.
• Ismail, M. E., & Zhang, R. (2017). A review of multivariate orthogonal polynomials. Journal of the Egyptian Mathematical Society, 25(2), 91-110.
• Orthogonal Polynomials in Mathematical Physics, from arXiv

Hypergeometric Series

• Hyperbolic Hypergeometric Functions, Fokko van de Bult

Basic Hypergeometric Series

• Applications of basic hypergeometric functions, GE Andrews - SIAM Review, 1974.
• Schlosser, M. J. (2017). Hypergeometric and basic hypergeometric series and integrals associated with root systems. arXiv preprint arXiv:1705.09221.
• Koelink, E. (2018). q-special functions, basic hypergeometric series and operators. arXiv preprint arXiv:1808.03441.

Elliptic Hypergeometric Series

• Spiridonov, V. P. (2008). Essays on the theory of elliptic hypergeometric functions. Russian Mathematical Surveys, 63(3), 405.
• Spiridonov, V. P. (2013). Aspects of elliptic hypergeometric functions. arXiv preprint arXiv:1307.2876.
• Rosengren, H. (2016). Elliptic hypergeometric functions. arXiv preprint arXiv:1608.06161.

Partitions

• Sieves in the theory of partitions, GE Andrews - American Journal of Mathematics, 1972.
• Partitions: yesterday and today, GE Andrews - New Zealand Mathematical Society, 1979.