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math.CV2021
On Taylor series of zeros with general base function
Mario DeFranco
We prove a formula for the Taylor series coefficients of a zero of the sum of a complex-exponent polynomial and a base function which is a general holomorphic function with a simpl…
math.CV2021
On Taylor series of zeros of complex-exponent polynomials
Mario DeFranco
We prove a factorization formula for the Taylor series coefficients of a zero of a polynomial as a function of the polynomial's coefficients. This result extends to more general fu…
math.CV2019
On the inequalities in Hermite's theorem for a real polynomial to have real zeros
Mario DeFranco
We prove expressions for the inequalities in Hermite's theorem which are conditions for a real polynomial to have real zeros. These expressions generalize the discriminant of a qua…