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The Weierstrass half‐periods  can be represented through the complete elliptic integral  and the inverse elliptic nome  by the formula:
The Weierstrass invariants  can be represented through the complete elliptic integral  , the inverse elliptic nome  , the modular lambda function  , and the theta functions  by the following formulas:
The Weierstrass  function values  at half-periods can be represented through the complete elliptic integral  , the modular lambda function  , the Weierstrass sigma function  , and the theta functions  by the following formulas:
The Weierstrass zeta function values at half-periods  can be represented through the complete elliptic integrals  and  , the modular lambda function  , and the theta functions  by the following formulas:
The following formula shows that the Weierstrass half‐periods  play the role of inverse functions to the Weierstrass invariants  :
The Weierstrass half‐periods  , the invariants  , and the Weierstrass  function values at half-periods  are connected by the following formulas:
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