nonvanishing

(mathematics) Of an expression, especially a function, being nonzero at a value, everywhere on a specified set, or on the entire domain.

2013-11-11, C. Herbert Clemens, A Scrapbook of Complex Curve Theory (University Series in Mathematics), Springer Science & Business Media, →ISBN, OCLC 1001480441, page 61:

This means that the vector space of solutions of (2.25) near 𝜆=0 is generated by

𝜎₁(𝜆) holomorphic and nonvanishing at 0,

(𝜆𝜎₂(𝜆)+(log𝜆)𝜎₁(𝜆)) where a 𝜎₂ is holomorphic and nonvanishing at 0.

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