Related papers: Landen inequalities for zero-balanced hypergeometr…
We review recent results on analytical properties (monotonicity and bounds) for ratios of contiguous functions of hypergeometric type. The cases of parabolic cylinder functions and modified Bessel functions have been discussed with…
We survey recent progress in a program aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-space ${\mathbb{R}}^n_{+}$ for second-order, homogeneous,…
In this paper the authors investigate a power mean inequality for a special function which is defined by the complete elliptic integrals.
R. K\"ustner proved in his 2002 paper that the function $w_{a,b,c}(z)=$ $F(a+1,b;c;z)/F(a,b;c;z)$ maps the unit disk $|z|<1$ onto a domain convex in the direction of the imaginary axis under some condition on the real parameters $a,b,c.$…
A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…
We present an algorithm for determining all inequivalent abelian symmetries of non-degenerate quasi-homogeneous polynomials and apply it to the recently constructed complete set of Landau--Ginzburg potentials for $N=2$ superconformal field…
In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.
In this paper we consider a new kind of inequality related to fractional integration, motivated by Gressman's paper. Based on it we investigate its multilinear analogue inequalities. Combining with the Gressman's work on multilinear…
We consider hyper- and superelliptic equations $f(x)=by^m$ with unknowns x,y from the ring of S-integers of a given number field K. Here, f is a polynomial with S-integral coefficients of degree n with non-zero discriminant and b is a…
We consider the integral operator $\mathcal{I}^{a,b,c}_{d,e}(f)(z)$ involving Clausen's Hypergeometric Function by means of convolution introduced by Chandrasekran and Prabhakaran for investigation. The conditions on the parameters $ a,b,…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one…
We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[{}_2F_1(a+\epsilon\lambda,b;c+\lambda;x),\qquad 0<x<1\] as $\lambda\to+\infty$ in the neigbourhood of $\epsilon x=1$ when the parameter $\epsilon>1$ and…
The properties of several functions are employed to investigate the zeros of the Riemann zeta function $\zeta(a+bi)$ $(0<a<1, b\neq 0)$. If the zeros of the zeta function have not the form $\frac{1}{2}+ib$ where $i=\sqrt{-1}$, we derive a…
Our interest lies in describing the zero behaviour of Gauss hypergeometric polynomials $F(-n,b; c; z)$ where $b$ and $c$ are arbitrary parameters. In general, this problem has not been solved and even when $b$ and $c$ are both real, the…
We find an integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace and cosine Fourier transforms. Using positivity conditions for the weight in this…
We establish a version of the Landen's transformation for Weierstrass functions and invariants that is applicable to general lattices in complex plane. Using it we present an effective method for computing Weierstrass functions, their…
In this paper, we first discuss the linear independence of the complete elliptic integrals of the first, second and third kinds $K(k)$, $E(k)$ and $\Pi(\mu(k),k)$, and then obtain an upper bound for the number of zeros of a function of the…
This paper investigates the generalized convexity properties of the Lambert $W$ function, defined as the solution to $W(z)e^{W(z)}=z$. Focusing on $H_{p,q}$-convexity and concavity with respect to H\"older means, we derive necessary and…
In this work, we derived the necessary and sufficient conditions on parameters for $_3F_2(^{a,b,c}_{b+1,c+1};z)$ Hypergeometric Function to be in the classes $\mathcal{M}^{\ast}(\lambda,\alpha)$ and $\mathcal{N}^{\ast}(\lambda,\alpha)$ and…
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)…