Related papers: Incomplete A-Hypergeometric Systems
Recently it has been shown that the $\alpha$-Sun density $h(x)$ [{\it J. Math. Anal. Appl.}, {\bf 527} (2023), p. 127371] which interpolates between the Fr{\'e}chet density and that of the positive, stable distributions whose density is…
We argue that the large discrete symmetry group of quantum Hall systems is insufficient in itself to determine the complete beta function for the scaling of the conductivities, $\sigma_{xx}$ and $\sigma_{xy}$. We illustrate this point by…
The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite…
The Wirtinger integral is one of the integral representations of the Gauss hypergeometric function. Its integrand is given by a product of complex powers of theta functions. We study the structure of the twisted homology and cohomology…
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…
The beta integral method proved itself as a simple nonetheless powerful method of generating hypergeometric identities at a fixed argument. In this paper we propose a generalization by substituting the beta density with a particular type of…
Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…
In this paper we evaluate integrals of products of gamma functions of Ramanujan type in terms of bilateral hypergeometric series. In cases where the bilateral hypergeometric series are summable, then we evaluate these integral as beta…
It is conjectured that a class of n-fold integral transformations {I(alpha)|alpha in {C}} forms a mutually commutative family, namely, we have I(alpha) I(beta)=I(beta) I(alpha) for all alpha, beta in {C}. The commutativity of I(alpha) for…
We generalize the known constructions of A-hypergeometric functions. In particular, we show that periods of middle dimension on affine or projective complex algebraic varieties are A-hypergeometric functions of coefficients of polynomial…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
In our recent work we proposed a generalization of the beta integral method for derivation of the hypergeometric identities which can by analogy be termed "the G function integral method". In this paper we apply this technique to the cubic…
The Sine Gordon theory is generalized to include several cosine terms. This is similar to the world sheet description of a string propagating in a tachyon background. This model is studied as a (boundary) 2d euclidean field theory and also…
By applying projection operators to state vectors of coordinates we obtain subspaces in which these states are no longer normalized according to Dirac's delta function but normalized according to what we call "incomplete delta functions".…
By a non-Gaussian integral we mean integral of the product of an arbitrary function and exponent of a polynomial. We develop a theory of such integrals, which generalizes and simplifies the theory of general hypergeometric functions in the…
We present a new expansion of the zeta-function of Riemann. The current formalism -- which combines both the idea of interpolation with constraints and the concept of hypergeometric functions -- can, in a natural way, be generalised within…
Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two…
The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact…
Several expansions of the solutions to the confluent Heun equation in terms of incomplete Beta functions are constructed. A new type of expansion involving certain combinations of the incomplete Beta functions as expansion functions is…