Derivative of Kummer's confluent hypergeometric with respect to parameter?

Asked May 09 '16 at 17:12

Active Aug 24 '17 at 07:09

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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

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

asked May 09 '16 at 17:12

a06e

6,665

2

This looks to do it: https://www.researchgate.net/publication/234904587_Derivatives_of_any_order_of_the_confluent_hypergeometric_function_1F1abz_with_respect_to_the_parameter_a_or_b – rrogers May 10 '16 at 13:04
For the derivative of ${_1F_1}\left(-\nu; 1; x\right)$ with respect to $\nu,$ see question Proving an identity involving the derivative of the Laguerre polynomials with respect to n – Olli Niemitalo Feb 27 '19 at 09:10

Derivative of Kummer's confluent hypergeometric with respect to parameter?

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