- #1
fred_91
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Homework Statement
I want to differentiate the Gauss hypergeometric function:
[itex]_2F_1[a,b;c;\frac{k-x}{z-x}][/itex]
with respect to z
Homework 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]
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.