Mathematics
Ali Shadhar's user avatar
Ali Shadhar's user avatar
Ali Shadhar's user avatar
Ali Shadhar
  • Member for 6 years, 6 months
  • Last seen this week
  • Phoenix, Arizona
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About

I have a Bachelor's degree in physics and I enjoy advanced calculus but my real interest goes to logarithmic/ polylogarithmic integrals and harmonic series.

I wrote a book about the harmonic series (An Introduction To The Harmonic Series And Logarithmic Integrals) and it's available on Amazon https://www.amazon.com/dp/1736736027

The eBook PDF can be found for free on the website https://www.harmonicnumber.com

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All Questions Answers
Score Newest
question
29
Are these generalizations known in the literature?
Mar 6, 2022
question
23
Challenging problem: Calculate $\int_0^{2\pi}x^2 \cos(x)\operatorname{Li}_2(\cos(x))dx$
Oct 7, 2020
question
20
Compute $\sum_{n=1}^\infty\frac{H_n^2H_n^{(2)}}{n^3}$
Aug 5, 2019
question
19
Challenging integral: Evaluate $\int_0^1\frac{\ln^3(1-x)\operatorname{Li}_3(x)}{x}dx$
Aug 7, 2019
question
18
How to find $\operatorname{P.V.}\int_0^1 \frac{1}{x (1-x)}\arctan \left(\frac{8 x^2-4 x^3+14 x-8}{2 x^4-3 x^3-11 x^2+16 x+16}\right) \textrm{d}x$?
Feb 1, 2021
question
17
Evaluating $\int_0^{\frac{\pi}{2}}x^2 \cot x\ln(1-\sin x)\mathrm{d}x$
Jan 25
question
16
How to approach $\sum _{n=1}^{\infty } \frac{16^n}{n^4 \binom{2 n}{n}^2}$?
Aug 20, 2020
question
16
Prove $ \int_0^1 \frac{\ln^a(1-x)\ln(1+x)}{x}dx=(-1)^a a! \sum_{n=1}^\infty\frac{H_n^{(a+1)}}{n2^n}$
Jul 14, 2019
question
16
Prove $\sum_{k=1}^\infty\frac{(-1)^{k-1}}{k^32^k {2k\choose k}}=\frac1{4}\zeta(3)-\frac1{6}\ln^32$
Jul 26, 2019
question
16
How to compute $\sum_{n=1}^\infty\frac{H_n^2}{n^32^n}$?
Aug 28, 2019
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40
What should I do when someone publishes a paper based on results I already posted on the internet?
7
How to approximate $PV\int_0^\infty \frac{\tan x}{x}\text{d}x?$
6
What's the Mathematica command for $\frac{\partial^a}{\partial n^a}\binom{n}{k}$?
5
How to get the right approximation for a series involving the harmonic number?
5
Why I get brackets different in the size?

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