arXiv subjects

Megumi Saigo

Publications and source records attributed to Megumi Saigo.

4 recordsLinked to original sources

arXiv1998

Integral transforms with H-function kernels on $\LLL_{ν,r}$-Spaces

Integral transforms $$(\mbox{\boldmath$H$}f)(x)=\int^\infty_0H^{m,n}_{\thinspace p,q} \left[xt\left|\begin{array}{c}(a_i,α_i)_{1,p}\\[1mm](b_j,β_j)_{1,q} \end{array}\right.\right]f(t)dt$$ involving Fox's $H$-functions as kernels are studied in the spaces $\Ls_{ν,r}$ of functions $f$ such that $$\int^\infty_0|t^νf(t)|^r\frac{dt}t<\infty\quad(1\ \eqls\ r<\infty, \ ν\in\Rs).$$ Mapping properties such as the boundedness, the representation and the range of the transforms \boldmath$H$ are given.

math.CA↗

arXiv1998

On the h-function

The paper is devoted to study the $H$-function defined by the Mellin-Barnes integral $$H^{m,n}_{\thinspace p,q}(z)={\frac1{2πi}}\int_{\Lss} \HHs^{m,n}_{\thinspace p,q}(s)z^{-s}ds,$$ where the function $\HH^{m,n}_{\thinspace p,q}(s)$ is a certain ratio of products of Gamma functions with the argument $s$ and the contour $\LL$ is specially chosen. The conditions for the existence of $H^{m,n}_{\thinspace p,q}(z)$ are discussed and explicit power and power-logarithmic series expansions of $H^{m,n}_{p,q}(z)$ near zero and infinity are given. The obtained results define more precisely the known results.

math.CA↗

arXiv1998

Expansions of _4F_3 when the upper parameters differ by integers

In this article three expansion formulas for a generalized hypergeometric function $_4F_3$ are derived, when its upper parameters differ by integers. Though the results are special cases of a general continuation formula for $_pF_q$, they are sufficiently general and unify a number of known results.

math.CA↗

arXiv1998

On inversion of H-Transform in $\eufb114_{ν,r}$-space

The paper is devoted to study the inversion of the integral transform $$(\mbox{\boldmath$H$}f)(x)=\int^\infty_0H^{m,n}_{\thinspace p,q} \left[xt\left|\begin{array}{c}(a_i,α_i)_{1,p}\\[1mm](b_j,β_j)_{1,q} \end{array}\right.\right]f(t)dt$$ involving the $H$-function as the kernel in the space $\euf114_{ν,r}$ of functions $f$ such that $$\int^\infty_0\left|t^νf(t)\right|^r\frac{dt}t<\infty\quad(1<r<\infty, \ ν\in\msb122).$$

math.CA↗