100 upvotes!

Calculus Level 5

\[ \large \int _{ 0 }^{ 1 }{ \dfrac {(\text{Li}_2(x) )^2 }{ { x }^{ 2 } } \, dx }=h\zeta (u)-n\zeta (d)-\dfrac { r }{ e } \zeta (d_1) \]

If the equation above holds true for positive integers \(h,u,n,d,r,e\) and \(d_1\), where \(r\) and \(e\) are coprime, find \(h+u+n+d+r+e+d_1\).

\[ \]

Notations:

  • \(\zeta(\cdot) \) denotes the Riemann zeta function.

  • \({ \text{Li} }_{ n }(a) \) denotes the polylogarithm function, \({ \text{Li} }_{ n }(a)=\displaystyle\sum _{ k=1 }^{ \infty }{ \dfrac { { a }^{ k } }{ { k }^{ n } } } \).

×

Problem Loading...

Note Loading...

Set Loading...