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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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How to write Tricomi's confluent hypergeometric function in terms of Meijer-G function
They are both correct.
Numerical check of the expression: $U(a,b,z) = \frac{G_{1,2}^{2,1}\left(z\left|\begin{smallmatrix}[1-a], [] \\
[0,1-b],[]\end{smallmatrix}\right.\right)}{\Gamma\left(a\right)\Ga …