Intereting Posts

Estimating partial sums $\sum_{n = 1}^m \frac{1}{\sqrt{n}}$
Show for prime numbers of the form $p=4n+1$, $x=(2n)!$ solves the congruence $x^2\equiv-1 \pmod p$. $p$ is therefore not a gaussian prime.
isomorphic planar graph with its complement
Any employment for the Varignon parallelogram?
What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$?
Looking for a proof for the following apparent relationships between the integral of survival and quantile functions with moments
Number of integer solutions of the following equation
Involutions and Abelian Groups
Groups of order $n^2$ that have no subgroup of order $n$
Mathematical induction prove that 9 divides $n^3 + (n+1)^3 + (n+2)^3$ .
Good Textbooks for Real Analysis and Topology.
Proof of Pythagorean theorem without using geometry for a high school student?
Can anyone extend my findings for Langford Pairings?
How can I determine the sequence generated by a generating function?
Why isn't this a valid argument to the “proof” of the Axiom of Countable Choice?

Euler’s constant has the following representations (Euler-Mascheroni constant expression, further simplification, https://math.stackexchange.com/a/129808/134791, Question on Macys formula for Euler-Mascheroni Constant $\gamma$)

$$

\gamma= \lim_{n \to \infty} {\left(2H_n-H_{n^2} \right)}=\sum_{n=1}^\infty \left(\frac{2}{n}-\sum_{j=(n-1)^2+1}^{n^2} \frac{1}{j}\right)

$$

$$

\gamma= \lim_{n \to \infty} {\left(2H_n-H_{n(n+1)} \right)}=\sum_{n=1}^\infty \left(\frac{2}{n}-\sum_{j=n(n-1)+1}^{n(n+1)} \frac{1}{j}\right)

$$

- When is right to kill $r^l$ and/or $r^{(-l-1)}$?
- Hermite Interpolation of $e^x$. Strange behaviour when increasing the number of derivatives at interpolating points.
- Is there an integral or series for $\frac{\pi}{3}-1-\frac{1}{15\sqrt{2}}$?
- Geometric explanation of $\sqrt 2 + \sqrt 3 \approx \pi$
- Prove that $y-x < \delta$
- Generalization of piece-wise linear functions over a metric space

$$

\gamma= \lim_{n \to \infty} {\left(2H_n-\frac{1}{6}H_{n^2+n-1}-\frac{5}{6}H_{n^2+n}\right)}$$$$=\frac{7}{12}+\sum_{n=1}^{\infty}\left(\frac{2}{n+1}-\frac{1}{3n(n+1)(n+2)}-\sum_{k=n(n+1)+1}^{(n+1)(n+2)}\frac{1}{k}\right)

$$

Hardy (1912) and Kluyver (1927) derived formulas for $\gamma_1$ and $\gamma_n ,n>1$ from Vacca’s formula for $\gamma$ (1910) (http://mathworld.wolfram.com/StieltjesConstants.html)

Q: How can formulas for Stieltjes constants be derived from the formulas above?

(See also Re-Expressing the Digamma)

- Geometric explanation of $\sqrt 2 + \sqrt 3 \approx \pi$
- Numerically Efficient Approximation of cos(s)
- Tensor products of functions generate dense subspace?
- Proof that $\frac{2}{3} < \log(2) < \frac{7}{10}$
- The right “weigh” to do integrals
- Does projection onto a finite dimensional subspace commute with intersection of a decreasing sequence of subspaces: $\cap_i P_W(V_i)=P_W(\cap_i V_i)$?
- A series to prove $\frac{22}{7}-\pi>0$
- About the first positive root of $\sum_{k=1}^n\tan(kx)=0$
- Elementary derivation of certian identites related to the Riemannian Zeta function and the Euler-Mascheroni Constant
- Can we prove the Riemann-Lebesgue lemma by using the Weierstrass approximation theorem?

- When does an irreducible polynomial stay irreducible as a power series?
- Generalized Fixed Point Theorem
- How can I prove the Carmichael theorem
- Does every Cauchy net of hyperreals converge?
- Determining ring of integers for $\mathbb{Q}$
- Sum of positive definite matrices still positive definite?
- last $2$ digit and last $3$ digit in $\displaystyle 2011^{{2012}^{2013}}$
- The ring of integers of the composite of two fields
- On the eigenvalues of a linear transformation $\tau$ such that $\tau^3 = \mathrm{id}$
- Semisimple Lie algebras are perfect.
- How to find surface normal of a triangle
- Where is the mistake in proving 1+2+3+4+… = -1/12?
- Questions related to intersections of open sets and Baire spaces
- Can I construct a complete (as a Boolean algebra) $\aleph_0$ saturated elementary extension of a given Boolean algbera?
- Where can I find SOLUTIONS to real analysis problems?