HALPHEN AND THE ELLIPTIC FUNCTIONS OF DU VAL

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Abstract We show that the ‘ternary’ elliptic functions that were introduced and studied by Du Val in 1964 are the $n=3$ instances of n -ary elliptic functions that are defined for arbitrary integers n greater than unity. We also trace the general n -ary elliptic function back to 1886 and the ‘fort remarquable’ function of Halphen.