Polygamma function
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In mathematics, the polygamma function of order m is a meromorphic function on the complex numbers C defined as the th derivative of the logarithm of the gamma function:
Complex Log Gamma
Complex Polygamma 0
Complex Polygamma 1
Complex Polygamma 2
Convex function
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In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph of the function between the two poin
Polygamma function
…Since both bounds are strictly positive for x > 0 , we have: ln Γ ( x ) is strictly convex. For m = 0 , the digamma function, ψ ( x ) = ψ ( 0 ) ( x ) , is strictly monotonic increasing and strictly concave…
Convex vs. not convex