Detailed work has produced a large body of plausible conjectures, for example about the exact type of functional equation that should apply.
22.
Therefore, use of the functional equation is basic, in order to study the zeta-function in the whole complex plane.
23.
In 1980's, he proved the theorem, using D . H . Hyers'propositions for solutions of functional equations.
24.
In view of the fact that multiplication of probabilities can be taken to be ordinary multiplication of real numbers, this becomes a functional equation
25.
With a little help from a functional equation for the Hurwitz zeta function, the polylogarithm is consequently also related to that function via:
26.
The functional equation alone will imply that " G " restricted to rational multiples of any particular number is an exponential function.
27.
FenyQ, along with Gian Luigi Forti, also found the solutions to the following inhomogeneous Cauchy functional equation in a Banach space E:
28.
In terms of functional analysis, Hamilton's principle states that the true evolution of a physical system is a solution of the functional equation
29.
Often this means that this function is a certain L-function and this gives an analytic continuation and functional equation for this L-function.
30.
M . Rassias led to the development of what is now known as "'Hyers Ulam Rassias stability "'of functional equations.
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