Tables of Special Functions
Many special functions appear as solutions of differential equations or integrals of elementary functions. Therefore, tables of integrals usually include descriptions of special functions, and tables of special functions include most important integrals; at least, the integral representation of special functions. Because symmetries of differential equations are essential to both physics and mathematics, the theory of special functions is closely related to the theory of Lie groups and Lie algebras, as well as certain topics in mathematical physics.
Symbolic computation engines usually recognize the majority of special functions. Not all such systems have efficient algorithms for the evaluation, especially in the complex plane.
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To every ticklish reader! Set them down
For sluttish spoils of opportunity
And daughters of the game.”
—William Shakespeare (1564–1616)
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