WeierstrassHalfPeriodW1

WeierstrassHalfPeriodW1[{g2,g3}]

gives the half-period ω1 for Weierstrass elliptic functions corresponding to the invariants {g2,g3}.

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The half-periods define the fundamental period parallelogram for the Weierstrass elliptic functions.
  • WeierstrassHalfPeriodW1 gives the first element ω1 returned by WeierstrassHalfPeriods.
  • WeierstrassHalfPeriodW1 can be evaluated to arbitrary numerical precision.

Examples

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Basic Examples  (3)

Evaluate numerically:

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Plot the real and imaginary parts of the first half-period:

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Compute the value of the Weierstrass function at the first half-period:

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Scope  (3)

Applications  (3)

Properties & Relations  (4)

See Also

WeierstrassHalfPeriodW2  WeierstrassHalfPeriodW3  WeierstrassHalfPeriods  WeierstrassP  WeierstrassE1  WeierstrassEta1

Tutorials

Introduced in 2017
(11.2)