For example, the j-invariant is a non-entire modular form of weight 0, and has a simple pole at i ".
12.
:"'Theorem ( Class Number Formula ) . "'function defined for all complex with only one simple pole at 1 } }, with residue
13.
These divergences turn out to be simple poles, but this part of complex analysis was not yet so developed at the time of Abel.
14.
Since such secular functions consist of a series of rational functions with simple poles, SRA is the best candidate to interpolate the zeros of the secular function.
15.
The Gamma function has a well defined power series expansions at each point of the positive real numbers ( it has a simple pole at zero ).
16.
A fishing pole is a simple pole or stick with a line which is fastened to the tip and suspended with a hooked bait at the other end.
17.
As a consequence, Leopoldt's conjecture for those fields is equivalent to their " p "-adic Dedekind zeta functions having a simple pole at " s " = 1.
18.
Also does anyone know of a proof that the residue of a simple pole is equal to lim ( z-c ) f ( z ) as z approaches z?
19.
Since \ zeta ( s ) has a simple pole at 1 } } and stays analytic, the left hand side in the previous inequality tends to 0, a contradiction.
20.
The masts and sails were removed after four years in service, and replaced by simple pole masts for carrying signal flags and circular fighting tops, platforms carrying quick firing guns.
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