Results 11 to 20 of about 162 (37)

The Mukhin-Varchenko conjecture for type A [PDF]

, 2008
International audienceWe present a generalisation of the famous Selberg integral. This confirms the $\mathfrak{g}=A_n$ case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for each simple Lie algebra $\mathfrak{g ...
Warnaar, S. Ole
core   +5 more sources

A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type [PDF]

, 2009
In this paper we consider a large class of many-variable polynomials which contains generalisations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the eigenfunctions of ...
Hallnäs, Martin, Langmann, Edwin
core   +3 more sources

Images for the Y‐Function via Marichev–Saigo–Maeda Fractional Integration and Differentiation Operators

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
The Y‐function has emerged as a significant tool in generalized fractional calculus due to its ability to unify and extend numerous classical special functions and hypergeometric‐type functions. Applying the Marichev–Saigo–Maeda fractional integration and differentiation operators of any complex order to the Y‐function, this study establishes four ...
Engdasew Birhane, D. L. Suthar, Shikha Binwal   +2 more
wiley   +1 more source

Some New Integral Formulas Involving the Product of Multivariable Aleph Function, General Class of Srivastava Polynomials, M‐Series, and Hypergeometric Functions

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Integral formulas play an important part in solving complicated scientific and technical problems. With this in mind, this study creates three essential formulas. These formulas include the product of the multivariable Aleph function, the general class of Srivastava’s polynomials, the M‐series, and hypergeometric functions.
Alok Bhargava, Komal Prasad Sharma, D. L. Suthar, G. Muhiuddin   +3 more
wiley   +1 more source

Deformed Complex Hermite Polynomials [PDF]

, 2014
We study a class of bivariate deformed Hermite polynomials and some of their properties using classical analytic techniques and the Wigner map. We also prove the positivity of certain determinants formed by the deformed polynomials. Along the way we also
Ali, S. Twareque, Ismail, Mourad E. H., Shah, Nurisya M.   +2 more
core  

A placebo‐controlled, double‐blind study evaluating the effect of orally administered polyunsaturated fatty acids on the oclacitinib dose for atopic dogs

Veterinary Dermatology, Volume 35, Issue 4, Page 408-417, August 2024.
Background – Supplementation of polyunsaturated fatty acids (PUFA) enables dose reduction of prednisolone and ciclosporin in canine atopic dermatitis (cAD). Objective – To determine if oral administration of PUFA can reduce the dose of oclacitinib for cAD. Conclusion – Oral supplementation of PUFA allowed dose reduction of oclacitinib and improved pVAS,
Laura Schäfer, Nina Thom
wiley   +1 more source

Evaluation of binomial double sums involving absolute values

, 2019
We show that double sums of the form $$ \sum_{i,j=-n} ^{n} |i^sj^t(i^k-j^k)^\beta| \binom {2n} {n+i} \binom {2n} {n+j} $$ can always be expressed in terms of a linear combination of just four functions, namely $\binom {4n}{2n}$, ${\binom {2n}n}^2$, $4^n ...
A Bostan, C Krattenthaler, C Schneider, C Schneider, HW Gould, J Hadamard, LJ Slater, M Karr, P Paule, RL Graham, RP Brent, RW Gosper   +11 more
core   +1 more source

On a Class of Generalized Elliptic-type Integrals [PDF]

, 2001
The aim of this paper is to study a generalized form of elliptic-type integrals which unify and extend various families of elliptic-type integrals studied recently by several authors.
Garg, Mridula, Kalla, S., Katta, Vimal
core  

A Selberg integral for the Lie algebra A_n

, 2007
A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every ...
A Lascoux, A Selberg, A Varchenko, A Varchenko, A Varchenko, CF Dunkl, E Mukhin, EM Opdam, EM Opdam, FG Garvan, G Gasper, GE Andrews, IG Macdonald, IG Macdonald, J Kaneko, J Kaneko, J Thomae, K Aomoto, K Mimachi, KWJ Kadell, L Euler, ML Mehta, PI Etingof, PJ Forrester, R Askey, RP Stanley, S. Ole Warnaar, SO Warnaar, TH Baker, V Tarasov, VV Schechtman   +30 more
core   +1 more source

On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions. [PDF]

Ramanujan J
Neretin YA.
europepmc   +1 more source