scholarly journals Various results in relation with the hypergeometric equations and the hypergeometric functions in the complex plane

2020 ◽  
Vol 65 (3) ◽  
pp. 345-356
Author(s):  
Huseyin Irmak ◽  
◽  
Keyword(s):  
Complex Plane ◽  
Hypergeometric Functions ◽  
Hypergeometric Equations

POLYNOMIALS ASSOCIATED WITH THE HYPERGEOMETRIC FUNCTIONS WITH FINITE MONODROMY GROUPS

2004 ◽  
Vol 15 (07) ◽  
pp. 629-649 ◽  
Author(s):  
HIROYUKI OCHIAI ◽  
MASAAKI YOSHIDA
Keyword(s):  
Hypergeometric Functions ◽  
Integral Parameter ◽  
Monodromy Groups ◽  
Hypergeometric Equations

The hypergeometric equations with polyhedral monodromy groups derive 3-integral-parameter families of polynomials.

scholarly journals The hodograph transformation in trans-sonic flow. II. Auxiliary theorems on the hypergeometric functions ψ n (ז)

1947 ◽  
Vol 191 (1026) ◽  
pp. 341-351 ◽  
Keyword(s):  
Differential Equation ◽  
Compressible Flow ◽  
Stream Function ◽  
Complex Plane ◽  
Hypergeometric Functions ◽  
Sonic Flow ◽  
In Trans ◽  
Hodograph Transformation

The applications of the theorems of this paper will be found in subsequent parts of this work. The author does not lay claim to originality for all of them, but believes that no connected account of the properties of ψ n (ז) as function of n in the complex plane has previously been given. The differential equation for the stream function in compressible flow is written, as in part I, in the form

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

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