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Kummer's confluent hypergeometric function is:

$$M(a,b;z)= {_1}F_1(a,b;z)$$

There is an easy recurrence for the derivative of $M$ with respect to $z$. I am interested in the derivative with respect to the parameters $a,b$. Are there any known relations involving

$$\frac{\partial M}{\partial a}, \quad \text{or} \quad \frac{\partial M}{\partial b}?$$

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