On a hypergeometric function of four variables with a new aspect ofSL-symmetry
Copyright policy )On a hypergeometric function of four variables with a new aspect ofSL-symmetry
The hypergeometric function under consideration is the author's \(K_{16}\). (It is also denoted by \(H_ C^{(4)}\).) A system of four partial differential equations for this function is obtained, and their singular manifolds are given. The system has 21 essentially different singular points in \(\mathbb{C}^ 4\). Some properties of \(K_{16}\) are given: an Euler transformation and a Pochhammer integral representation. Next, it is shown that the system of PDE's has further solutions in terms of \(K_{16}\) and two more quadruple hypergeometric functions. After these preparations the author can finally present, for each of the 21 singularities, a list of six linearly independent integrals of the system of PDE's. The expressions are too long to reproduce here.
Other hypergeometric functions and integrals in several variables, hypergeometric PDE's, bisingularities for PDE's
Other hypergeometric functions and integrals in several variables, hypergeometric PDE's, bisingularities for PDE's
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