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Jul
18
accepted Ratio of sum of Euler's totient to $n$: $\lim_{n \to \infty} {\log \left( \sum_{k=2}^n \varphi(k) \right) \over \log(n)}$
Jul
17
accepted Problem with infinite product using iterating of a function: $ \exp(x) = x \cdot f^{\circ 1}(x)\cdot f^{\circ 2}(x) \cdot \ldots $
Jul
15
accepted How can I prove that an iterated transformation describes all odd integers?
May
20
accepted What is the functional inverse (with respect to $h$ (!)) of $f^{\circ h}(x)={F(h) +x F(h-1) \over F(1+h) +x F(h) }$?
May
15
accepted Half order derivative of $ {1 \over 1-x }$
May
8
accepted $f(x)=\tanh(1+\tanh^{-1}(x))$ or $f:\tanh(x) \to \tanh(x+1)$ is a rational function?
Apr
16
accepted Sum of the Stieltjes constants? (divergent summation)
Apr
5
accepted Exercising divergent summations: $\lim 1-2+4-6+9-12+16-20+\ldots-\ldots$
Mar
10
accepted Having $A_1=a+b+c$,$A_2=a^2+b^2+c^2$, $A_3=a^3+b^3+c^3$ - how to get $a,b,c$?
Feb
20
accepted How can I prove my conjecture for the coefficients in $t(x)=\log(1+\exp(x)) $?
Jan
21
accepted How to relate this integral for the $\Gamma$ function to the defining integral of the $\Gamma$
Jan
15
accepted Convergence radius of $\log(\Gamma(\exp(x)))$?
Jan
3
accepted Is my shorter expression for $ s_m(n)= 1^m+2^m+3^m+\cdots+(n-1)^m \pmod n$ true?
Dec
28
accepted What is the derivative of a power series composed with a sum of iterations on x?
Dec
11
accepted When is $1+x+x^2+x^3+… $ and $ {1 \over 1-x} \quad (x \ne 1) $ *not* interchangeable in an algebraic formula?
Oct
2
accepted $(2k+1)^{4k+1} = (2k+1) \pmod {4k+2} $ . . . why?
Aug
3
accepted Polynomial coefficients in exponential-series: how can I convert this into a composite of $\exp(x)$?
Aug
2
accepted Something like : “recursive” harmonic numbers? Where can I read more?
Aug
2
accepted What is the correct terminology to say that $\small f(x)=a+bx+cx^2+…$ can be expressed by $\small g(x)=A(1-x)+B(1-x)(2-x)+C(1-x)(2-x)(3-x)+… $
Jul
2
accepted How can “ $\small {n \over \varphi(n) } \text{ is integer only if } n=2^r \cdot 3^s $ ” simply be shown?