Zobrazeno 1 - 10
of 16 491
pro vyhledávání: '"Sum Sum"'
We are interested in finding an explicit estimate to the binomial sum $Q_n(x)=\sum_{k=0}^{n} k! {n\choose k}^2 (-x)^{k}$ at $x=1$ for $n=0,1,2,\ldots$. Despite of its own interest the polynomial $Q_n(x)$ is important as the denominator in the Pad\'e
Externí odkaz:
http://arxiv.org/abs/2310.11468
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
Autor:
Jolany, Hassan
In this short note, we give an identity for the $\alpha$ function $$\alpha(x,s)=\sum_{n=0}^\infty\frac{x^n}{(n!)^s}$$ where $s\in \mathbb{N}$, $x\in \mathbb{R}$, in the case $s=3$.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/1809.10607
We evaluate the convolution sum $\displaystyle W_{a,b}(n):= \sum_{al+bm=n} \hspace{-3mm} \sigma(l) \sigma(m)$ for $(a,b)=(1,28), (4,7), (2,7)$ for all positive integers $n$. We use a modular form approach. We also re-evaluate the known sums $W_{1,14}
Externí odkaz:
http://arxiv.org/abs/1607.06039
Autor:
Paris, R. B.
We obtain an asymptotic expansion for the sum \[S(a;w)=\sum_{n=1}^\infty \frac{e^{-an^2}}{n^{w}}\] as $a\rightarrow 0$ in $|\arg\,a|<\pi/2$ for arbitrary finite $w>0$. The result when $w=2m$, where $m$ is a positive integer, is the analogue of the we
Externí odkaz:
http://arxiv.org/abs/1501.00685
Autor:
Mattarei, Sandro
We prove that $\sum_{k=0}^{q-1}\binom{2k}{k}\equiv q^2\pmod{3q^2}$ if q>1 is a power of 3, as recently conjectured by Z.W. Sun and R. Tauraso. Our more precise result actually implies that the value of $(1/q^2)\sum_{k=0}^{q-1}\binom{2k}{k}$ modulo a
Externí odkaz:
http://arxiv.org/abs/1001.2156
Autor:
Bender, David A
Publikováno v:
A Dictionary of Food and Nutrition, 4 ed., 2014.
Externí odkaz:
http://www.oxfordreference.com/view/10.1093/acref/9780191752391.001.0001/acref-9780191752391-e-5269
Autor:
Bender, David A
Publikováno v:
A Dictionary of Food and Nutrition, 3 ed., 2009.
Externí odkaz:
http://www.oxfordreference.com/view/10.1093/acref/9780199234875.001.0001/acref-9780199234875-e-5269
Autor:
Soykan Y
In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}W_{k}^{2}$ \ for the squares of generalized Tetranacci numbers are presented. We also present the sum formulas $\sum_{k=0}^{n}W_{k+1}W_{k},$ $\sum_{k=0}^{n}W_{k+2}W_{k},$ and $\sum_{k=0}^
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::82ec4e1b18623201cd2db3d411e68beb
https://doi.org/10.20944/preprints202005.0453.v1
https://doi.org/10.20944/preprints202005.0453.v1
Autor:
Yavuz Kesicioğlu, Şaban Alaca
Publikováno v:
Funct. Approx. Comment. Math. 61, no. 1 (2019), 27-45
We determine the convolution sum $\sum_{al+bm=n} \sigma(l) \sigma(m)$ for $(a,b)=(1,48), (3, 16), (1,54), (2,27)$ for all positive integers $n$. We then use these evaluations together with known evaluations of other convolution sums to determine the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::49ec0706045b4eaeb381ce5cb2475132
https://projecteuclid.org/euclid.facm/1543460438
https://projecteuclid.org/euclid.facm/1543460438