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 generalized exponential integral function, $\Gamma(u,s)$ upper incomplete gamma function $k\in \mathbb{N}$.

a total of 260709 monthly test day milk records of 30903 first lactation holstein cows was used to determine the best function to describe the lactation curve. the records were obtained from first lactation holstein of 216 herds from 1988 to 2006 in khorasan province. the functions used in current study were wood’s incomplete gamma function, ali and schaeffer function, and legendre function of ...

The objectives were to estimate (co)variance components and genetic parameters for lactation curve traits in Holstein dairy cows in Iran. The used data were records on Holstein cows collected during January 2003 to December 2012 by the Animal Breeding Center of Iran (Karaj, Iran). In order to describe the lactation curve, an incomplete gamma function was fitted to 691200 test-day records on 962...

h thii paper, an asymptotic expression of the incomplete gamma matrix function and integral expressions of Bessel matrix functions are given. Results are applied to study the asymptotic behavior of the modified Bessel function. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords-Bessel function, Incomplete gamma function, Asymptotics.

We derive the infinite sum of Lerch function in terms incomplete gamma and function. Special cases are evaluated fundamentals constants. All results this work new.

In this paper, some recursive relations of the derivatives of the gamma function Γ(α) and incomplete gamma function Γ(α, z) are obtained for complex number α ̸= 0,−1,−2, · · ·. Moreover, the recurrence relation of the derivative of the k−gamma function Γk(x) are also given. Thus, the partial derivative ∂ p+q ∂νp∂μq B(ν, μ) of the Beta function B(ν, μ) can also be represented for p, q = 0, 1, 2, ...