Related papers: On quotients and differences of hypergeometric fun…
In 1984, the second author conjectured a quadratic transformation formula which relates two hypergeometric 2F1 functions over a finite field F_q. We prove this conjecture and give an application. The proof depends on a new linear…
In this paper our aim is to present some Landen inequalities for Gaussian hypergeometric functions, confluent hypergeometric functions, generalized Bessel functions and for general power series. Our main results complement and generalize…
The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.
We provide a sharp upper bound on the quotient of the rank of an A-hypergeometric system with a three-dimensional torus action by the normalized volume of A; in this case, the upper bound is two.
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
Let $K$ be a square in the plane and $\rho_K(x,y)$ be the hyperbolic distance between $x$, $y\in K$. Denote by $s_K(x,y)$ the triangular ratio metric in $K$; for $x\neq y$ the value of $s_K(x,y)$ equals the ratio of the Euclidean distance…
We derive all eighteen Gauss hypergeometric representations for the Ferrers function of the second kind, each with a different argument. They are obtained from the eighteen hypergeometric representations of the associated Legendre function…
The scheme for construction of distances, presented in the previous paper quant-ph/0005087, v.1 (Ref. 1) is amended. The formulation of Proposition 1 of Ref. 1 does not ensure the triangle inequality, therefore some of the functionals…
In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hypergeometric' algebraic varieties that are higher dimensional…
We give an upper bound for the error term in the Hardy-Ramanujan-Rademacher formula for the partition function. The main input is a new hybrid subconvexity bound for the central value $L(\tfrac 12,f\times (\tfrac{q}{\cdot}))$ in the $q$ and…
We will present some (formal) arguments that any Feynman diagram can be understood as a particular case of a Horn-type multivariable hypergeometric function. The advantages and disadvantages of this type of approach to the evaluation of…
A lower bound for the Gaussian Q-function is presented in the form of a single exponential function with parametric order and weight. We prove the lower bound by introducing two functions, one related to the Q-function and the other…
Let $F(X,Y)=Y^d+a_1(X)Y^{d-1}+...+a_d(X)$ be a polynomial in $n+1$ variables $(X,Y)=(X_1,...,X_n,Y)$ with coefficients in an algebraically closed field K. Assuming that the discriminant $D(X)=\disc_Y F(X,Y)$ is nonzero we investigate the…
It is shown how to define difference operators and equations on particular lattices $\{x_n\}$, $2n\in\mathbb{Z}$, such that the divided difference operator $(\mathcal{D}f)(x_{n+1/2})= (f(x_{n+1})-f(x_n))/(x_{n+1}-x_n)$ has the property that…
In this paper, the connection between the functional inequalities $$ f\Big(\frac{x+y}{2}\Big)\leq\frac{f(x)+f(y)}{2}+\alpha_J(x-y) \qquad (x,y\in D)$$ and $$ \int_0^1f\big(tx+(1-t)y\big)\rho(t)dt \leq\lambda f(x)+(1-\lambda)f(y)…
We obtain the asymptotic expansion for the Gauss hypergeometric function \[F(a-\lambda,b+\lambda;c+i\alpha\lambda;z)\] for $\lambda\rightarrow+\infty$ with $a$, $b$ and $c$ finite parameters by application of the method of steepest…
We prove explicit formulas for certain first and second moment sums of families of Gaussian hypergeometric functions $_{n+1}F_n$, $n\ge1$, over finite fields with $q$ elements where $q$ is an odd prime. This enables us to find an estimate…
Humbert confluent hypergeometric functions of two variables arise in many problems of mathematical physics and applied analysis, yet their behavior with respect to parameters has not been systematically studied. In this paper we investigate…
We study the character sums \[\phi_{(m,n)}(a,b)=\sum_{x\in\mathbb{F}_q}\phi\left(x(x^{m}+a)(x^{n}+b)\right),\textrm{ and, } \psi_{(m,n)}(a,b)=\sum_{x\in\mathbb{F}_q}\phi\left((x^{m}+a)(x^{n}+b)\right)\] where $\phi$ is the quadratic…
In this paper a double integral containing two Gaussian hypergeometric functions is discussed. The integral is not found in the literature and a direct computation is not (yet) possible. Therefore, a complete different integral is computed…