scholarly journals A HARMONIC MEAN INEQUALITY CONCERNING THE GENERALIZED EXPONENTIAL INTEGRAL FUNCTION

2021 ◽  
Vol 10 (9) ◽  
pp. 3227-3231
Author(s):  
Kwara Nantomah
Keyword(s):  
Gamma Function ◽  
Integral Function ◽  
Incomplete Gamma Function ◽  
Harmonic Mean ◽  
Exponential Integral

In this paper, we prove that for $s\in(0,\infty)$, the harmonic mean of $E_k(s)$ and $E_k(1/s)$ is always less than or equal to $\Gamma(1-k,1)$. Where $E_k(s)$ is the generalized exponential integral function, $\Gamma(u,s)$ is the upper incomplete gamma function and $k\in \mathbb{N}$.

scholarly journals Refinements of Some Recent Inequalities for Certain Special Functions

2019 ◽  
Vol 33 (1) ◽  
pp. 1-20
Author(s):  
Mohamed Akkouchi ◽  
Mohamed Amine Ighachane
Keyword(s):  
Gamma Function ◽  
Generalized Inverse ◽  
Special Functions ◽  
Integral Function ◽  
Inverse Gaussian ◽  
Exponential Integral ◽  
Generalized Inverse Gaussian Distribution ◽  
Normalizing Constant ◽  
Lerch Zeta Function ◽  
Generalized Inverse Gaussian

AbstractThe aim of this paper is to give some refinements to several inequalities, recently etablished, by P.K. Bhandari and S.K. Bissu in [Inequalities via Hölder’s inequality, Scholars Journal of Research in Mathematics and Computer Science, 2 (2018), no. 2, 124–129] for the incomplete gamma function, Polygamma functions, Exponential integral function, Abramowitz function, Hurwitz-Lerch zeta function and for the normalizing constant of the generalized inverse Gaussian distribution and the Remainder of the Binet’s first formula for ln Γ(x).

ON THE INCOMPLETE GAMMA FUNCTION AND ITS NEUTRIX CONVOLUTION FOR NEGATIVE INTEGERS

2019 ◽  
Vol 10 (1) ◽  
pp. 30-51
Author(s):  
Mongkolsery Lin ◽  
◽  
Brian Fisher ◽  
Somsak Orankitjaroen ◽  
◽  
...  
Keyword(s):  
Gamma Function ◽  
Incomplete Gamma Function
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