Weierstrass sigma function
In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function
called 'pe'.
Weierstrass sigma function
The Weierstrass sigma function is defined as the product
: where denotes and
is the two-dimensional lattice.
Weierstrass zeta function The Weierstrass zeta function is defined by the sum
: Note that the Weierstrass zeta function is basically the logarithmic derivative of the sigma function. The zeta function can be rewritten as:
:
where is the Eisenstein series of weight . Also note that the derivative of the zeta function is .
Weierstrass eta function The Weierstrass eta function is defined to be
: It can be proved that this is well defined, i.e. only depends on w. The Weierstrass eta function should not be confused with the Dedekind eta function.
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