Abstract
At first only elementary functions were studied in mathematical analysis. Then new functions were introduced to evaluate integrals. They were named special functions: integral sine, logarithms, the exponential function, the probability integral and so on. Elliptic integrals proved to be the most important. They are connected with rectification of arcs of certain curves. The remarkable idea of Abel to replace these integrals by the corresponding inverse functions led to the creation of the theory of elliptic functions.
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Klimyk, A.U., Vilenkin, N.Y. (1995). Representations of Lie Groups and Special Functions. In: Kirillov, A.A. (eds) Representation Theory and Noncommutative Harmonic Analysis II. Encyclopaedia of Mathematical Sciences, vol 59. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09756-4_2
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