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We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
An explicit transformation formula for chiral conformal fields under arbitrary holomorphic coordinate transformations is established. As an application I calculate the transformation law of the general quasiprimary field at level 4.
In a previous work ([Eb]), the author proposed a method employing contiguity relations to derive hypergeometric series in closed form. In [Eb], this method was used to derive Gauss's hypergeometric series $_2F_1$ possessing closed forms.…
In many cases one may encounter an integral which is of $q$-Mellin--Barnes type. These integrals are easily evaluated using theorems which have a long history dating back to Slater, Askey, Gasper, Rahman and others. We derive some…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
A complete characterization of two functions $f(x,y)$ and $g(x,y)$ in the $(f,g)$-inversion is presented. As an application to the theory of hypergeometric series, a general bibasic summation formula determined by $f(x,y)$ and $g(x,y)$ as…
Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a…
We produce two-dimensional contiguous relations for generalized hypergeometric functions by starting with linearization coefficients for some continuous generalized hypergeometric orthogonal polynomials in the Askey-scheme.
Motivated by our previous work on hypergeometric functions and the parbelos constant, we perform a deeper investigation on the interplay among generalized complete elliptic integrals, Fourier-Legendre (FL) series expansions, and ${}_p F_q$…
Motivated by the work on hypergeometric summation theorems (recorded in the table III of Prudnikov et al. pp. 541-546), we have established some new summation theorems for Clausen's hypergeometric functions with unit argument in terms of…
The partial sums of two quartic basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several summation and transformation formulae are consequently established.
Miller-Paris transformations are extensions of Euler's transformations for the Gauss hypergeometric functions to generalized hypergeometric functions of higher-order having integral parameter differences (IPD). In our recent work we…
A summation formula is derived for the sum of the first m+1 terms of the 3F2(a,b,c;(a+b+1)/2,2c;1) series when c = -m is a negative integer. This summation formula is used to derive a formula for the sum of a terminating double…
In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
Ismail and Wilson derived a generating function for Askey--Wilson polynomials which is given by a product of $q$-Gauss (Heine) nonterminating basic hypergeometric functions. We provide a generalization of that generating function which…
In this present paper our aim is to deal with two integral transforms which involving the Gauss hypergeometric function as its kernels. We prove some compositions formulas for such a generalized fractional integrals with k Bessel function.…
Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the $p$-Laplacian, which is known as a typical nonlinear differential operator. Compared to GTFs with…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
We present some integral transform that allows to obtain solutions of the generalized Tricomi equation from solutions of a simpler equation. We used in [13,14],[41]-[46] the particular version of this transform in order to investigate in a…