I. R. Lomidze and N. V. Makhaldiani
abstract:
A generalization of the Euler beta function for the case of multi-dimensional
variable is proposed. In this context ordinary beta function is defined as a
function of two-dimensional variable. An analogue of the Euler formula for this
new function is proved for arbitrary dimension. There is found out the
connection of defined function with multi-dimensional hypergeometric
Laurichella's function and the theorem on cancelation of multi-dimensional
hypergeometric functions singularities is proved. Such generalizations (among
others) may be helpful to construct corresponding physical (string) models
including different number of fields, as far the (bosonic) string theory
reproduces the Euler beta function (Veneziano amplitude) and its
multi-dimensional analogue.
Mathematics Subject Classification: 33B15, 33C65, 81T30
Key words and phrases: Generalized Euler integrals, multivariable hypergeometric functions, strings theory