(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I want to differentiate the Gauss hypergeometric function:

[itex]_2F_1[a,b;c;\frac{k-x}{z-x}][/itex]

with respect to z

2. Relevant equations

The derivative of

[itex]_2F_1[a,b;c;z][/itex]

with respect to z is:

[itex]\frac{ab}{c} _2F_1[1+a,1+b;1+c;z][/itex]

3. The attempt at a solution

Can I treat this as any other function, i.e., the same as with z in the fourth parameter but multiplied by the derivative of the fourth parameter:

[itex]\frac{ab}{c} _2F_1[a,b;c;\frac{k-x}{z-x}]\frac{-(k-x)}{(z-x)^2}[/itex]

If the fourth parameter was sin(z). Would the derivative of

[itex]_2F_1[a,b;c;\sin(z)][/itex]

with respect to z

be

[itex]\frac{ab}{c} _2F_1[1+a,1+b;1+c;sin(z)]cos(z)[/itex]?

Thank you in advance.

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# Homework Help: Gauss hypergeometric function derivative

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