= Confluent hypergeometric function of the first kind
{title2=$M(a,b,z)={}_1F_1(a;b;z)$}
= Kummer function
{c}
{synonym}
For $b$ not a nonpositive integer, the regular solution normalized by $M(a,b,0)=1$ has the <power series>
$$
M(a,b,z)=\sum_{n=0}^{\infty}\frac{(a)_n}{(b)_n}\frac{z^n}{n!}.
$$
Here $(a)_n$ is the <rising factorial>. Substitution into the <Kummer differential equation> proves the coefficient recurrence. This normalization agrees with https://dlmf.nist.gov/13.2[NIST's definitions].
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