ترغب بنشر مسار تعليمي؟ اضغط هنا

Some new formulas for the Horns hypergeometric functions

96   0   0.0 ( 0 )
 نشر من قبل Ayman Shehata
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

The aim of this work is to demonstrate various an interesting recursion formulas, differential and integral operators, integration formulas, and infinite summation for each of Horns hypergeometric functions $mathrm{H}_{1}$, $mathrm{H}_{2}$, $mathrm{H}_{3}$, $mathrm{H}_{4}$, $mathrm{H}_{5}$, $mathrm{H}_{6}$ and $mathrm{H}_{7}$ by the contiguous relations of Horns hypergeometric series. Some interesting different cases of our main consequences are additionally constructed.



قيم البحث

اقرأ أيضاً

Inspired by the recent work Sahin and Agha gave recursion formulas for $mathcal{G}_{1}$ and $mathcal{G}_{2}$ Horn hypergeometric functions cite{saa}. The object of work is to establish several new recursion relations, relevant differential recursion formulas, new integral operators, infinite summations and interesting results for Horns hypergeometric functions $mathcal{G}_{1}$, $mathcal{G}_{2}$ and $mathcal{G}_{3}$.
403 - V.P. Spiridonov 2016
This is a brief overview of the status of the theory of elliptic hypergeometric functions to the end of 2012 written as a complementary chapter to the Russian edition of the book by G.E. Andrews, R. Askey, and R. Roy, Special Functions, Encycl. of Math. Appl. 71, Cambridge Univ. Press, 1999.
Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second commutator $[ D,[D,U]]$ is proportional to $U$. Operators $D=d/dx$ (differentiation) and $U$- multiplication by $e^{lambda x}$ or by $sin lambda x$ are basic examples, for which some of these relations appeared unexpectedly as byproducts of an authors previous medical imaging research.
198 - Raimundas Vidunas 2011
Gauss hypergeometric functions with a dihedral monodromy group can be expressed as elementary functions, since their hypergeometric equations can be transformed to Fuchsian equations with cyclic monodromy groups by a quadratic change of the argument variable. The paper presents general elementary expressions of these dihedral hypergeometric functions, involving finite bivariate sums expressible as terminating Appells F2 or F3 series. Additionally, trigonometric expressions for the dihedral functions are presented, and degenerate cases (logarithmic, or with the monodromy group Z/2Z) are considered.
The conical function and its relativistic generalization can be viewed as eigenfunctions of the reduced 2-particle Hamiltonians of the hyperbolic Calogero-Moser system and its relativistic generalization. We prove new product formulas for these funct ions. As a consequence, we arrive at explicit diagonalizations of integral operators that commute with the 2-particle Hamiltonians and reduc
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا