Tagging - 2020-08-03

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5:04 AM

The tag multiple-zeta-functions contains two questions at the moment:

Q: Fourier Legendre expansion for $\frac{\text{Li}_2(x)}{x},\frac{\log ^2(1-x)}{x},\frac{\log (x) \log (1-x)}{x}$

Background: I'm trying to compute some harmonic sums using Fourier Legendre expansion. For instance, the following expansion $$\frac{\log (1-x)}{x}=\sum _{n=0}^{\infty } 2 (-1)^{n-1} (2 n+1) P_n(2 x-1) \left(\sum _{k=n+1}^{\infty } \frac{(-1)^{k-1}}{k^2}\right)$$ can be used to compute $\sum_{n=1...

Q: A remarkable logarithmic integral $\int_0^1 \frac{\log^2 (1-x) \log^2 x \log^3(1+x)}{x} dx$

Two years ago, I discovered the following neat result:$$\tag{*}\small{ \int_0^1 \frac{\log^2 (1-x) \log^2 x \log^3(1+x)}{x} dx = -168 \text{Li}_5\left(\frac{1}{2}\right) \zeta (3)+96 \text{Li}_4\left(\frac{1}{2}\right){}^2-\frac{19}{15} \pi ^4 \text{Li}_4\left(\frac{1}{2}\right)+\\ 12 \pi ^2 \tex...

integration sequences-and-series zeta-functions polylogarithm multiple-zeta-functions

@pisco As far as I can tell, you've created the (multiple-zeta-functions) tag. I just wanted to let you know about the related post on meta: math.meta.stackexchange.com/questions/31103/tag-management-2‌020/… — Martin Sleziak 10 secs ago

The tag was created on July 20: chat.stackexchange.com/transcript/3740/2020/7/20

I have notified the tag-creator, in case they want to comment on this. — Martin Sleziak 6 secs ago

5 hours later…

user185131

9:58 AM

→ 8 messages moved to In continued pursuit of moksha

Martin Sleziak

12:53 PM

new-tag A new tag first-order-condition was created by YJT.

Q: First Order Condition with 1 decision variable and 2D state space

TL;DR: I'm trying to find the first-order condition (FOC) for an optimization problem with two state variables and one control variable. I don't want the value function $V$ to appear in the FOC but can't get rid of it. Help is highly appreciated. $\def\d{\delta} \def\b{\beta} \def\g{\gamma} \def\...