On the Analytic Extension of Functions Defined by Double Power Series
نویسنده
چکیده
defining a function f(x, y) of the two independent complex variables x, y within the regions | x | < i?,, | y \ < R2 ( Rx > 0, R2 > 0 ), to determine the value of this function at any point in its domain of existence, f It is our special purpose to demonstrate the following theorem : Theorem. If in the series (1) the function a(u, v) considered as a function of the two independent, complex variables u, v(u — a + iß, v = y + ih) is single valued and analytic for those values of u, v for which a = 0, 7 = 0 and if there exists a constant c such that for the same values of u,v
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