DLMF:25.11.E45

MaRDI QIDQ8412

• Label: DLMF:25.11.E45

Digital Library of Mathematical Functions ID 25.11.E45

${\displaystyle{\displaystyle\zeta'\left(-2,a\right)-\frac{1}{12}a+\frac{1}{9}a^{3}-\left(\frac{1}{6}a-\frac{1}{2}a^{2}+\frac{1}{3}a^{3}\right)\ln a\sim\sum_{k=1}^{\infty}\frac{2B_{2k+2}}{(2k+2)(2k+1)2k(2k-1)}a^{-(2k-1)}.}}$

Symbols List

• ${\displaystyle{\displaystyle B_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$: Hurwitz zeta function
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
 

Resources that cite this formula

No records found.