Steven Clark's user avatar
Steven Clark's user avatar
Steven Clark's user avatar
Steven Clark
  • Member for 7 years, 5 months
  • Last seen this week
11 votes
Accepted

Can a functional equation of the form: $\zeta (s)=f(s) \zeta (s+1)$ exist?

6 votes

An entire function interpolating $\mu(n)$

5 votes
Accepted

What is Relationship Between Distributional and Fourier Series Frameworks for Prime Counting Functions?

4 votes

Riemann's explicit formula for $\pi(x)$

4 votes

Is the largest gap between consecutive primes less than the first $27,000$ integers equal to $52?$

4 votes
Accepted

Evaluate $\int_0^\infty \sum^{\lfloor x\rfloor}_{n=1}\frac{\sin nx\pi}{x^n}dx$

4 votes

Is my proof of $\eta(0)=\frac{1}{2}$ correct?

4 votes
Accepted

How well does $\mathrm{Zi}(x)=\frac1e\sum_{k=1}^\infty\frac{(\ln x)^k}{kk!\phi(k)}$, with $\phi(k)=\sum_{n=1}^\infty e^{-n^k}$, approximate $\pi(x)$?

4 votes
Accepted

Calculate the integral $\int\limits_{0}^{\infty }\frac{x^{s}}{\sqrt{x^2+1}}dx$

4 votes
Accepted

Is it possible to Expand the Dirac Delta function into the summation of a serie of certain Bessel functions?

3 votes

Is it possible to extend the prime counting function $\pi(x)$ to all real numbers like with the factorials?

3 votes
Accepted

How can the relation of the Riemann Zeta Function (for natural arguments) to the Generalized Hypergeometric Function be proven / derived?

3 votes
Accepted

Verification of the generalized polylogarithm formula

3 votes
Accepted

Fourier series expansion of $\delta(x-1)$

3 votes
Accepted

Motivation for the Derivative of an Arithmetic Function

3 votes

Hankel transform of exponential involving square root argument without HT

3 votes
Accepted

What is the value of the composite zeta function evaluated at 2?

3 votes
Accepted

Laplace transform of cosine

3 votes
Accepted

Logarithmic integral, complex, argument, several answers?

3 votes
Accepted

Verifying a Fourier series inverting $\frac{\tan(y)}y$ with the Whittaker W function

3 votes
Accepted

Asymptotic behavior of the summatory Liouville function

2 votes
Accepted

Divergence of the Derivative of the Prime Counting Function

2 votes

Mellin space convolution and usual convolution

2 votes

Do you know a name and expression of this function of Lehmer?

2 votes

Is (Inverse) Fourier Transform still a "sum" of sinusoids?

2 votes
Accepted

$\frac{1}{2 \pi a} \int_{-\pi a}^{\pi a} \exp \left(-\frac{1}{2} \left( \frac{2 a \sin^{-1} \left( \frac{x}{2 a} \right)}{\sigma} \right)^2 \right)dx$

2 votes
Accepted

What is the primorial development of e ?(the notion of "primorial development" is defined in the body)

2 votes
Accepted

Deriving the Integral for Alternating Harmonic Series Partial Sums

2 votes
Accepted

How to find $\mathrm{\sum_{n=1}^\infty E_{n}(n)= \lim_{k\to\infty}\int_1^\infty \frac{e^{kt+t}t^k-e^t}{e^{kt+2t}t^{k+1}-e^{kt+t}t^k}dt=.26929…}$?

2 votes

Branch cuts and continuity of $f(z) = \sqrt{z^2-1}$ while visualizing it

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