The leading root of the partial theta function
Abstract
I study the leading root x0(y) of the partial theta function 0(x,y) = Σn=0∞ xn yn(n-1)/2, considered as a formal power series. I prove that all the coefficients of -x0(y) are strictly positive. Indeed, I prove the stronger results that all the coefficients of -1/x0(y) after the constant term 1 are strictly negative, and all the coefficients of 1/x0(y)2 after the constant term 1 are strictly negative except for the vanishing coefficient of y3.
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