The functional equation can be written in a form which
is more symmetric:
The -function associated to a general -function is similar, except that the factor is omitted, since its only purpose was to cancel the pole at .
The function just involves a change of variables: . The functional equation now asserts that .
The Hardy -function is defined as follows. Let
Plots of are a nice way to picture the -function on the critical line. is called RiemannSiegelZ[t] in Mathematica.
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