Judyxcheng
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1. The problem statement, all variables and given/known
I have taken the limit of both sides of an equation for x going toward infinity. There is a digamma (psi(x)) function on the RHS, and the limit of the term is supposed to be (at least close to) 0. Thus, the term can cancel out.
My professor said that indeed, the digamma function is supposed to be around 0 for large arguments and he wants me to justify that with the digamma function's integral form. However, when I research digamma online, it appears to slowly diverge or converge to a number larger than 0. Can someone clarify this?
Integral form of digamma function, found here where it says "The digamma function satisfies": http://mathworld.wolfram.com/DigammaFunction.html
I have taken the limit of both sides of an equation for x going toward infinity. There is a digamma (psi(x)) function on the RHS, and the limit of the term is supposed to be (at least close to) 0. Thus, the term can cancel out.
My professor said that indeed, the digamma function is supposed to be around 0 for large arguments and he wants me to justify that with the digamma function's integral form. However, when I research digamma online, it appears to slowly diverge or converge to a number larger than 0. Can someone clarify this?
Homework Equations
Integral form of digamma function, found here where it says "The digamma function satisfies": http://mathworld.wolfram.com/DigammaFunction.html