Izvorni znanstveni članak
https://doi.org/10.21857/y6zolb7wwm
Generalized Horn function \(H_{4,p,q,\nu}^\lambda\) and related bounding inequalities with applications to statistics
Rakesh K. Parmar
; Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry-605014, India
Tibor K. Pogány
orcid.org/0000-0002-4635-8257
; Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary
S. Pirivina
orcid.org/0009-0007-4036-1811
; Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry-605014, India
Sažetak
Motivated by recent unified version of the Euler's Beta integral form with a MacDonald function in the integrand,
we generalize the Horn double hypergeometric function \(H_4[x,y]\). We then establish integral representations of the Euler
and Laplace type including some other representations involving Bessel \(J_\nu(z)\) and modified Bessel functions \(I_\nu(z)\) for
the generalized Horn double hypergeometric function \(H_{4,p,q,\nu}^\lambda\). Several functional upper bounds for the
\(H_{4,p,q,\nu}^\lambda\) including the extended Gaussian hypergeometric \(F_{p,q,\nu}^\lambda\), the extended Kummer's
confluent hypergeometric \(\Phi_{p,q,\nu}^\lambda\) are obtained by using functional bounds for extended Euler's Beta function
\({\rm B}_{p,q,\nu}^\lambda(x,y)\). Various other bounding inequalities are obtained via Luke's, von Lommel's, Minakshisundaram
and Szász and Olenko bounds. As an application, we define a Horn hypergeometric probability distribution to obtain certain
statistical interference.
Ključne riječi
Extended Beta function; Extended hypergeometric function; Extended confluent hypergeometric function; Horn double hypergeometric function H_4; Bessel and modified Bessel functions; functional bounding inequalities; probability distribution; Turán inequalities
Hrčak ID:
344366
URI
Datum izdavanja:
10.2.2026.
Posjeta: 250 *