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Parity of EllipticTheta


I use quite often the functions EllipticTheta[n,x,q] in Mathematica. Unlike for trigonometric functions Mathematica does not simplify expressions of the type EllipticTheta[1,-x,q] to -EllipticTheta[1,x,q] automatically (it does it for Sin[-x]). How do I add such a feature to a built-in function?

Thank you in advance,

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