Appell-Kamp� de F�riet hypergeometric functions of two variables

Asymmetric Modulation for Hardware Impaired Systems—Error Probability Analysis and Receiver Design

“…where the weights ω k (y k ) and ω l (x l ) are obtained using (35). Moreover, y k and x l are the k th and l th zeros of the K th −order Legendre polynomial P K (y) and L th −order Legendre polynomial P L (x) respectively.…”

On the Regge–Gelfand Problem of Construction of a Pfaff System of Fuchsian Type with a Given Singular Divisor

“…A similar construction takes place for functions F 2 , F 3 [5]. The singular divisor for F 2 is x = 0, y = 0, x = 1, y = 1, x + y = 1, and for F 3 is x = 0, y = 0, x = 1, y = 1, xy − x − y = 0.…”

“…The singular set of the function F 4 (α, β, γ, γ ; x, y) is x 2 + y 2 + 1 − 2x − 2y − 2xy = 0, x = 0, y = 0 (see [5]). …”

“…(3) in astronomy, cosmology and general relativity, (4) in differential geometry, (5) in mathematical physics, (6) in the theory of nonlinear waves, etc. The structure of this section is the following: we describe the reduction procedure for the simplest cases of ordinary differential equations and then consider two methods of applications of Fuchsian reduction to astronomy and general relativity.…”

“…(α + n − 1). A Pfaffian system type associated with F 4 is given in the paper [5]. Some other Pfaffian system was given by Kato [13].…”