How to learn Digamma Function and how to take derivative of Gamma function?

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How can I learn polygamma function?(More precisely digamma function)As I was learning Bessel Function of Second kind expressed in terms of power series digamma function is used.I have firm-grasp in Calculus(Single and Multivariable).But no exposure to Complex Analysis.Is it necessary to have idea in Calculus of Complex variable to learn Gamma function completely?Can we expressed power series of Bessel Function of Second kind without using diagamma function using it factorial notation and how to derive it?