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On a functional equation for the exponential function of a complex variable
Published online by Cambridge University Press: 18 May 2009
Extract
The following result is well known in the theory of analytic functions; see [1].
Theorem A. Suppose that f(z) is an entire function of a complex variable z. Then f(z) satisfies the functional equation
where z = x + iy (x, y real), if and only if f(z) = aexp(sz), where a is an arbitrary complex constant and s is an arbitrary real constant.
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- Copyright © Glasgow Mathematical Journal Trust 1971
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