The Fresnel formulae presented in the parent entry- that the proof refers to- are as follows:
(visible there only in the Tex code mode because of a current quirk/glitch with pstricks vs. Tex).
The remainder of the equations Tex mode correctly specified by pahio in the parent entry entitled Fresnel formulae is precisely quoted here as follows:
“The function
is entire, whence by the fundamental theorem
of complex analysis we have
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(1) |
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(2) |
For handling
, we use the substitution
Using also de Moivre's formula we can write
Comparing the graph of the function
Hence we obtain
and moreover
Therefore
Then make to
the substitution
It yields
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|
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(3) |
So we get also the result
As of this snapshot date, this entry was owned by bci1.