Congruence relations for p-adic hypergeometric functions $$\widehat{{\mathscr {F}}}_{a,...,a}^{(\sigma )}(t)$$ and its transformation formula
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DOI: 10.1007/s00229-021-01327-1
Abstract: We introduce new kind of $p$-adic hypergeometric functions. We show these functions satisfy congruence relations, so they are convergent functions. And we show that there is a transformation formula between our new $p$-adic hypergeometric functions… read more here.
Keywords: transformation formula; hypergeometric functions; adic hypergeometric; congruence relations ... See more keywords
Geometric Properties of the Shifted Hypergeometric Functions
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DOI: 10.1007/s11785-017-0674-4
Abstract: We will provide sufficient conditions for the shifted hypergeometric function $$z_2F_1(a,b;c;z)$$z2F1(a,b;c;z) to be a member of a specific subclass of starlike functions in terms of the complex parameters a, b and c. For example, we study… read more here.
Keywords: hypergeometric functions; shifted hypergeometric; properties shifted; order alpha ... See more keywords
Some hypergeometric functions in positive characteristic and transcendence
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DOI: 10.1016/j.crma.2019.03.006
Abstract: Abstract In this work, we study some special hypergeometric functions in positive characteristic, introduced by D. S. Thakur. We shall establish functional relationships among them, and deduce, with the help of the function field version… read more here.
Keywords: hypergeometric functions; functions positive; characteristic transcendence; positive characteristic ... See more keywords
Sharp Landen transformation inequalities for hypergeometric functions, with applications
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DOI: 10.1016/j.jmaa.2019.02.018
Abstract: Abstract The authors present sharp Landen transformation inequalities for the hypergeometric functions F 1 2 ( a , b ; a + b ; x ) and F 1 2 ( a , b ;… read more here.
Keywords: hypergeometric functions; transformation inequalities; landen transformation; inequalities hypergeometric ... See more keywords
On integral representations and asymptotics of some hypergeometric functions in two variables
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DOI: 10.1080/10652469.2017.1404596
Abstract: ABSTRACT The leading asymptotic behaviour of the Humbert functions , , of two variables is found, when the absolute values of the two independent variables become simultaneously large. New integral representations of these functions are… read more here.
Keywords: two variables; hypergeometric functions; integral representations; functions two ... See more keywords
Horn's hypergeometric functions with three variables
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DOI: 10.1080/10652469.2020.1814770
Abstract: The work is devoted to obtaining explicit formulas for analytic continuation of quite general hypergeometric series depending on three variables and belonging to the Horn class. We have derived such continuation formulas with respect to… read more here.
Keywords: three variables; hypergeometric functions; continuation; horn hypergeometric ... See more keywords
Fundamental Solutions of the Generalized Helmholtz Equation with Several Singular Coefficients and Confluent Hypergeometric Functions of Many Variables
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DOI: 10.1134/s1995080220010047
Abstract: Abstract An investigation of applied problems related to heat conduction and dynamics, electromagnetic oscillations and aerodynamics, quantum mechanics and potential theory leads to the study of various hypergeometric functions. The great success of the theory… read more here.
Keywords: confluent hypergeometric; hypergeometric functions; fundamental solutions; solutions generalized ... See more keywords
Rational Points over Finite Fields on a Family of Higher Genus Curves and Hypergeometric Functions
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DOI: 10.11650/tjm.21.2017.7724
Abstract: In this paper we investigate the relation between the number of rational points over a finite field $\mathbb{F}_{p^n}$ on a family of higher genus curves and their periods in terms of hypergeometric functions. For the… read more here.
Keywords: hypergeometric functions; genus curves; points finite; family higher ... See more keywords
Degenerate binomial coefficients and degenerate hypergeometric functions
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DOI: 10.1186/s13662-020-02575-3
Abstract: In this paper, we investigate degenerate versions of the generalized p th order Franel numbers which are certain finite sums involving powers of binomial coefficients. In more detail, we introduce degenerate generalized hypergeometric functions and… read more here.
Keywords: degenerate hypergeometric; hypergeometric functions; binomial coefficients; numbers order ... See more keywords
On basic Horn hypergeometric functions H 3 $\mathbf{H}_{3}$ and H 4 $\mathbf{H}_{4}$
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DOI: 10.1186/s13662-020-03056-3
Abstract: The purpose of this work is to demonstrate several interesting contiguous function relations and q -differential formulas for basic Horn hypergeometric functions H 3 $\mathbf{H}_{3}$ and H 4 $\mathbf{H}_{4}$ . Some properties of our main… read more here.
Keywords: hypergeometric functions; horn hypergeometric; basic horn; functions mathbf ... See more keywords
Some Summation Theorems for Generalized Hypergeometric Functions
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DOI: 10.3390/axioms7020038
Abstract: Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we… read more here.
Keywords: summation; generalized hypergeometric; hypergeometric functions; theorems generalized ... See more keywords