Results 41 to 50 of about 936 (88)

Defining Incomplete Gamma Type Function with Negative Arguments and Polygamma functions $ψ^{(n)}(-m)$ [PDF]

arXiv, 2014
In this paper the incomplete gamma function $\gamma(\alpha,x)$ and its derivative is considered for negative values of $\alpha $ and the incomplete gamma type function $\gamma_*(\alpha,x_-)$ is introduced. Further the polygamma functions $\psi^{(n)}(x)$ are defined for negative integers via the neutrix setting.
arxiv  

An Asymptotic relation for Hadjicostas Formula [PDF]

arXiv, 2009
We derive an asymptotic formula which in some cases generalize Hadjicostas ...
arxiv  

Some completely monotonic functions involving the polygamma functions [PDF]

arXiv, 2010
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
arxiv  

On Solving Some Trigonometric Series [PDF]

, 2013
This communication shows the track for finding a solution for a sin(kx)/k**2 series and a fresh representation for the Euler's Gamma function in terms of Riemann's Zeta function.
Stenlund, Henrik
core  

A probabilistic approach to some binomial identities [PDF]

arXiv, 2011
Classical binomial identities are established by giving probabilistic interpretations to the summands. The examples include Vandermonde identity and some generalizations.
arxiv  

New Upper Bounds in the Second Kershaw's Double Inequality and its Generalizations [PDF]

, 2007
In the paper, new upper bounds in the second Kershaw’s double inequality and its generalizations involving the gamma, psi and polygamma functions are established, some known results are ...
Guo, Senlin, Qi, Feng
core  

Applications of Neutrix Calculus to Special Functions in Conjunction with Polygamma Functions [PDF]

arXiv, 2014
In this paper we define the polygamma functions $\psi^{(n)}(x)$ for negative integers by using neutrix calculus.
arxiv  

An alternating proof of sharp inequalities related with Burnside's formula [PDF]

arXiv, 2019
We provide an alternating proof of sharp inequalities related with Burnside's formula for $n!$
arxiv  

Some Inequalities for the Ratios of Generalized Digamma Functions

, 2014
Some inequalities for the ratios of generalized digamma functions are presented. The approache makes use of the series representations of the $(q,k)$-digamma and $(p,q)$-digamma functions.Comment: 5 ...
Nantomah, Kwara
core   +1 more source

A surprising property of nonlocal operators: the deregularising effect of nonlocal elements in convolution differential equations

Advanced Nonlinear Studies
We consider nonlocal differential equations with convolution coefficients of the form−M(a*|u|q)(1)μ(t)u″(t)=λft,u(t), t∈(0,1), $$-M\left(\left(a {\ast} \vert u{\vert }^{q}\right)\left(1\right)\mu \left(t\right)\right){u}^{{\prime\prime}}\left(t\right ...
Goodrich Christopher S.
doaj   +1 more source