Balanced polygamma function: Difference between revisions

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* <math>\Gamma(x)=e^{\psi(-1,x)+\frac 12 \ln(2\pi)}</math>
 
 
* <math>\zeta(z,q)=\frac{\Gamma (1-z) \left(2^{-z} \left(\psi \left(z-1,\frac{q}{2}+\frac{1}{2}\right)+\psi \left(z-1,\frac{q}{2}\right)\right)-\psi(z-1,q)\right)}{\ln(2)}</math>
 
 
* <math>B_n(q) = -\frac{n \Gamma (n) \left(2^{n-1} \left(\psi\left(-n,\frac{q}{2}+\frac{1}{2}\right)+\psi\left(-n,\frac{q}{2}\right)\right)-\psi(-n,q)\right)}{\ln (2)}</math>
 
==References==