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+--- Thread: Problem with cauchy method ? (/showthread.php?tid=955)
Problem with cauchy method ? - tommy1729 - 02/16/2015
The Cauchy method has the property/condition (assum it works) :
exp(f(-1 +ai)) = f(ai)
exp(f(ai)) = f(1+ai)
for real a.
But is that sufficient to conclude f(z+1) = exp(f(z)) ?
Compare to x sin(x/2 pi) for integer x.
However the answer is YES ITS SUFFICIENT.
Because exp(f(-1 +ai)) - f(ai) = 0 and then use analytic continuation.
But what about the theta wave ? How do we know we arrive at a (unique) solution that is bounded in the strip ?
regards
tommy1729