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As in the title, I am looking for a single word meaning "the property of being holomorphic".

The obvious candidates are "holomorphy" and "holomorphicity" but both look wrong to my eye. "Holomorphism" would seem to mean "a holomorphic function" rather than referring to the property itself.

As an analogy, the phrase "because $f$ is continuous" can be rephrased as "by the continuity of $f$". I would like a word that I can use to rephrase "because $f$ is holomorphic" as "by the ________ of $f$".

In SAT notation:

continuous : continuity :: holomorphic : ?

(This almost belongs on English.SE but I am specifically interested in idiomatic usage in mathematical writing rather than textbook grammar, if they conflict.)

Edit: Regarding the suggestions to use "analyticity" or "complex differentiability", we have been using "holomorphic" consistently through the rest of the paper and I think it would be confusing to switch. Moreover, my understanding is that "analytic" refers specifically to being representable as a power series - in our paper we are working on a complex manifold, so this notion isn't immediately applicable.

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  • $\begingroup$ (NB speaking not as a complex analyst) holomorphicity feels the most familiar, but in writing I would probably avoid the point altogether and write complex-analyticity, or just analyticity if context allowed. $\endgroup$ Commented Sep 30, 2014 at 14:47
  • $\begingroup$ What does grammar say it should be, anyway? $\endgroup$
    – Git Gud
    Commented Sep 30, 2014 at 14:47
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    $\begingroup$ I use "holomorphicity". I'm pretty sure I've also read that in the literature. Also it rhymes with analyticity. $\endgroup$ Commented Sep 30, 2014 at 14:52
  • $\begingroup$ Personally, I would probably avoid all of the above and write "complex differentiability". $\endgroup$ Commented Sep 30, 2014 at 14:56
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    $\begingroup$ @GitGud, I don’t believe that there is any “rule” that applies. (After all this is English!) $\endgroup$
    – Lubin
    Commented Sep 30, 2014 at 17:19

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In several complex variables there is a standard term domain of holomorphy. Hardly anyone ever writes "domain of holomorphicity".

However, outside of "domain of" combination, both holomorphicity and holomorphy are about equally used. My feeling is that people using complex analysis in relation to Banach spaces, Lie groups, etc are more likely to write holomorphy, while traditional complex analysts are more likely to write holomorphicity. (As a special case of the latter, I would write holomorphicity myself.)

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  • $\begingroup$ is holomorphicity vs holomorphy perhaps like gold vs golden or mystic vs mystical? $\endgroup$
    – BCLC
    Commented Oct 11, 2021 at 19:25

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