The invariants of a Weierstrass elliptic function are defined by the Eisenstein series
(1)
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(2)
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Here,
(3)
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where and are the half-periods of the elliptic function. The Wolfram Language command WeierstrassInvariants[omega1, omega2] gives the invariants and corresponding to the half-periods and .
Writing ,
(4)
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(5)
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and the invariants have the Fourier series
(6)
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(7)
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where is the half-period ratio and is the divisor function (Apostol 1997).