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# Questions tagged [hypergeometric-functions]

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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### Uniform Asymptotic Approximation of the Whittaker function

I would like to know if there exist a uniform asymptotic approximation of the Whittaker function $W_{\kappa,i\mu}(x)$ for $\kappa<0$, $x >0$, and with $\mu \to +\infty$. The case of \$\kappa \ge ...

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