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In mathematics, the quarter periods K and iK ′ are special functions that appear in the theory of elliptic functions.
The quarter periods K and iK ′ are given by
and
When m is a real number, 0 < m < 1, then both K and K ′ are real numbers. By convention, K is called the real quarter period and iK ′ is called the imaginary quarter period. Any one of the numbers m, K, K ′, or K ′/K uniquely determines the others.
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