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Results tagged with hypergeometric-functions
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user 160051
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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Accepted
Proving Clausen hypergeometric identity
Let
$$y_1(z):={}_2F_1\left(a, b; a+b+\frac{1}{2}; z\right)^2$$
and
$$ y_2(z):= {}_3F_2\left(2a, 2b, a+b; a+b+\frac{1}{2}, 2a+2b, z\right) $$
You can verify that $y_1$ and $y_2$ both satisfy the follow …
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