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→Connection with Laguerre polynomials and similar representations: Added another representation via Laguerre polynomials |
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:<math>M\left(a,b,\frac{x y}{x-1}\right) = (1-x)^a \cdot \sum_n\frac{a^{(n)}}{b^{(n)}}L_n^{(b-1)}(y)x^n</math> {{harv|Erdélyi|Magnus|Oberhettinger|Tricomi|1953|loc=6.12}}
or
:<math>\operatorname{M}\left( a;\, b;\, z \right) = \frac{\Gamma\left( 1 - a \right) \cdot \Gamma\left( b \right)}{\Gamma\left( b - a \right)} \cdot \operatorname{L_{-a}^{b - 1}}\left( z \right)</math>[https://functions.wolfram.com/HypergeometricFunctions/Hypergeometric1F1/27/01/0001/]
==Special cases==
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