Zobrazeno 1 - 10
of 85
pro vyhledávání: '"Primary 33C20"'
For a given positive integer $m$, the concept of {\it hyperdeterminantal total positivity} is defined for a kernel $K:\R^{2m} \to \R$, thereby generalizing the classical concept of total positivity. Extending the fundamental example, $K(x,y) = \exp(x
Externí odkaz:
http://arxiv.org/abs/2412.03000
We give a formula for the cyclotomic valuation of $q$-Pochhammer symbols in terms of (generalized) Dwork maps. We also obtain a criterion for the $q$-integrality of basic hypergeometric series in terms of certain step functions, which generalize Chri
Externí odkaz:
http://arxiv.org/abs/2209.11075
We develop a $D-$module approach to various kinds of solutions to several classes of important differential equations by long divisions of different differential operators. The zeros of remainder maps of such long divisions are handled by an analogue
Externí odkaz:
http://arxiv.org/abs/2111.05103
Autor:
Assaf Samer, Cuchta Tom
Publikováno v:
Demonstratio Mathematica, Vol 56, Iss 1, Pp 1291-1307 (2023)
Discrete analogues of the sine integral and complementary exponential integral functions are investigated. Hypergeometric representation, power series, and Laplace transforms are derived for each. The difficulties in extending these definitions to ot
Externí odkaz:
https://doaj.org/article/1ce1b0e4c09c45eabe1d7dffe782b0e8
Autor:
Gaunt, Robert E.
Simple upper and lower bounds are established for the integral $\int_0^x\mathrm{e}^{-\beta u}u^\nu t_{\mu,\nu}(u)\,\mathrm{d}u$, where $x>0$, $0<\beta<1$, $\mu+\nu>-2$, $\mu-\nu\geq-3$, and $t_{\mu,\nu}(x)$ is the modified Lommel function of the firs
Externí odkaz:
http://arxiv.org/abs/2103.16666
Autor:
Gaunt, Robert E.
Publikováno v:
Proceedings of the American Mathematical Society 149 (2021), pp. 3889-3904
Simple upper and lower bounds are established for the integral $\int_0^x\mathrm{e}^{-\beta t}t^\nu \mathbf{L}_\nu(t)\,\mathrm{d}t$, where $x>0$, $\nu>-1$, $0<\beta<1$ and $\mathbf{L}_\nu(x)$ is the modified Struve function of the first kind. These bo
Externí odkaz:
http://arxiv.org/abs/2101.11247
Autor:
Adam, Alexander
We study the incomplete Mellin transformation of the fractional part and the related log-sine function when composed by an affine complex map. We evaluate the corresponding integral in two different ways which yields equalities with series in hyperge
Externí odkaz:
http://arxiv.org/abs/2009.07134
Autor:
Au, Kam Cheong
We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some infinite seri
Externí odkaz:
http://arxiv.org/abs/2007.03957
Autor:
Gaunt, Robert E.
We establish some monotonicity results and functional inequalities for modified Lommel functions of the first kind. In particular, we obtain new Tur\'{a}n type inequalities and bounds for ratios of modified Lommel functions of the first kind, as well
Externí odkaz:
http://arxiv.org/abs/2002.07430
General series identities, some additive theorems on hypergeometric functions and their applications
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are generally app
Externí odkaz:
http://arxiv.org/abs/1902.06690