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Results tagged with hypergeometric-functions
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user 30390
Hypergeometric functions are the analytic functions defined by Taylor expansions of the shape $\sum_{n \geq 0} a_n x^n$, where $a_{n+1}/a_n$ is a rational function of $n$. This general family of functions encompasses many classical functions. The hypergeometric functions play an important role in many parts of mathematics.
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Sharp upper bounds on hypergeometric function ${}_2F_1[a,b,c;z]$ when $|z|\geq1$
For the asymptotic analysis of hypergeometric functions, perhaps the Barnes contour integral representation is a more powerful tool than the series expansion. The book The special functions and their …
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Is a basic hypergeometric function ${}_2\phi_1(a, b; c; q, z)$ a meromorphic function in $z$?
Here a basic hypergeometric function is the analytic continuation of the basic hypergeometric series (or called the $q$-hypergeometric series)
$$
{}_2\phi_1(a, b; c; q, z) = \sum^{\infty}_{n = 0} \fr …
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