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Gauss hypergeometric function derivative

  1. Jun 18, 2012 #1
    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.
     
  2. jcsd
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