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Search Results: 1 - 10 of 104242 matches for " Chao-Ping Chen "
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Sharpness of Muqattash-Yahdi problem
Chen, Chao-Ping;Mortici, Cristinel;
Computational & Applied Mathematics , 2012, DOI: 10.1590/S1807-03022012000100005
Abstract: let ψ denote the psi (or digamma) function. we determine the values of theparameters p, q and r such that ψ(n) ≈ ln(n + p) - is the best approximations. also, we present closer bounds for psi function, which sharpens some known results due to muqattash and yahdi, qi and guo, and mortici. mathematical subject classification: 33b15, 26d15.
Improving some sequences convergent to Euler-Mascheroni constant
Batir,Necdet; Chen,Chao-Ping;
Proyecciones (Antofagasta) , 2012, DOI: 10.4067/S0716-09172012000100004
Abstract: we obtain the very fast sequences convergent to euler-mascheroni constant.
Certain relationships among Polygamma functions, Riemann Zeta function and Generalized Zeta function
Junesang Choi and Chao-Ping Chen
Journal of Inequalities and Applications , 2013, DOI: 10.1186/1029-242X-2013-75
Abstract: Many useful and interesting properties, identities, and relations for the Riemann Zeta function $\zeta (s)$ and the Hurwitz Zeta function $\zeta (s,a)$ have been developed. Here, we aim at giving certain (presumably) new and (potentially) useful relationships among Polygamma functions, Riemann Zeta function and Generalized Zeta function by modifying Chen's method. We also present a double inequality approximating $\zeta (2r+1)$ by a more rapidly convergent series.
Note on Alzer's inequality
Chao-Ping Chen,Feng Qi
Tamkang Journal of Mathematics , 2006, DOI: 10.5556/j.tkjm.37.2006.11-14
Abstract: If the sequence $ {a_i }_{i=1}^{infty} $ satisfies $ riangle a_i=a_{i+1}-a_i<0$, $ riangle^2 a_i= riangle( riangle a_{i})=a_{i+2}-2a_{i+1}+a_{i}geqslant0 $, $ i=0,1,2,ldots $, $ a_0=0 $. Then $$ frac{a_n}{a_{n+1}}< left(frac{1}{a_n}sum_{i=1}^{n}a_{i}^{r}igg / frac{1}{a_{n+1}}sum_{i=1}^{n+1}a_{i}^{r} ight)^{1/r} $$ for all natural numbers $ n $, and all real $ r>0$.
New proofs of monotonicities of generalized weighted mean values
Chao-Ping Chen,Feng Qi
Tamkang Journal of Mathematics , 2004, DOI: 10.5556/j.tkjm.35.2004.301-304
Abstract: Two new proofs of monotonicities with either $r$, $s$ or $x$, $y$ of the generalized weighted mean values $M_{p,f}(r,s;x,y)$ are given.
Generalization of an inequality of Alzer for negative powers
Chao-Ping Chen,Feng Qi
Tamkang Journal of Mathematics , 2005, DOI: 10.5556/j.tkjm.36.2005.219-222
Abstract: Let $ {a_n }_{n=1}^{infty} $ be a positive, strictly increasing, and logarithmically concave sequence satisfying $ (a_{n+1}/a_{n})^{n}<(a_{n+2}/a_{n+1})^{n+1} $. Then we have $$frac {a_n}{a_{n+m}} where $ n $, $ m $ are natural numbers and $ r $ is a positive real number. The lower bound is the best possible. This generalizes an inequality of Alzer for negative powers.
Extension of an Inequality of H. Alzer for Negative Powers
Chao-Ping Chen,Feng Qi
Tamkang Journal of Mathematics , 2005, DOI: 10.5556/j.tkjm.36.2005.69-72
Abstract: In this paper, we show that let $n$ be a natural number, then for all real numbers $ r $, $$ frac{n}{n+1} Both bounds are best possible. This extends a result of H. Alzer, who established this inequality for $ r>0 $.
Completely monotonic function associated with the Gamma functions and proof of Wallis' inequality
Chao-Ping Chen,Feng Qi
Tamkang Journal of Mathematics , 2005, DOI: 10.5556/j.tkjm.36.2005.303-307
Abstract: We prove: (i) A logarithmically completely monotonic function is completely monotonic. (ii) For $ x>0 $ and $ n=0, 1, 2, ldots $, then $$ (-1)^{n}left(ln frac{x Gamma(x)}{sqrt{x+1/4},Gamma(x+1/2)} ight)^{(n)}>0. $$ (iii) For all natural numbers $ n $, then $$ frac1{sqrt{pi(n+4/ pi-1)}}leq frac{(2n-1)!!}{(2n)!!} The constants $ frac{4}{pi}-1$ and $frac14 $ are the best possible.
A double inequality for remainder of power series of tangent function
Chao-Ping Chen,Feng Qi
Tamkang Journal of Mathematics , 2003, DOI: 10.5556/j.tkjm.34.2003.351-356
Abstract: By mathematical induction, an identity and a double inequality for remainder of power series of tangent function are established.
Improving some sequences convergent to Euler-Mascheroni constant
Necdet Batir,Chao-Ping Chen
Proyecciones (Antofagasta) , 2012,
Abstract: We obtain the very fast sequences convergent to Euler-Mascheroni constant.
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