I would like to know which variant is correct:

  1. "Decimal expansion of the first generalized Euler's constant"
  2. "Decimal expansion of first generalized Euler's constant"
  3. "Decimal expansion of the first generalized Euler constant"

The problem is the presence of "the" and the genitive "'s".

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  • 1
    First is an old superlative (that's where the final st) comes from, and like all superlatives, it is definite and unique, so a definite article is in order. As to the possessive, that depends. Is there a "generalized Euler's constant"? If not, then the fact that there are possibly several of them and reference to only one would suggest that the first generalized Euler constant is the correct phrasing. But it depends on how mathematicians view it. – John Lawler Mar 18 '15 at 21:18
  • 1
    What @john said. But missing articles are a standard feature of newspaper "headlinese" - and by association, technical report titles. – FumbleFingers Mar 18 '15 at 21:20
  • @John Lawler Thank you! Yes, there may be several generalized Euler's constants, i.e. first generalized Euler's constant, second generalized Euler's constant, etc. I took Euler as an example. The actual problem is to know if I can say "Decimal expansion of the first Malmsten's integral" or, should I say, "Decimal expansion of first Malmsten's integral"... Malmsten was a (great) Swedish mathematician. The problem is that one usually says "Fourier series", but also "Kummer's transformation"... – Iaroslav Mar 18 '15 at 21:25
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    So you can then say things like Riemann's Hypothesis states that the real part of all non-trivial zeros of the generalized Riemann zeta function equals -½. Riemann gets a genitive for the hypothesis but not for the function. – John Lawler Mar 18 '15 at 21:58
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    @JohnLawler Thank you for your very detailed explanations, it is much more clear now! Your exampe with Riemann is awesome! – Iaroslav Mar 20 '15 at 19:43

Disclaimer: English is not my native language, although I live in the U.S.

Personally, I would write it as

the decimal expansion of the first generalized Euler constant

But I believe this is not the only acceptable way. I see no problems while reading

the decimal expansion of the first generalized Euler's constant

But dropping "the" before "first" sounds wrong.

See http://mathworld.wolfram.com/Euler-MascheroniConstant.html for examples.


The best way to say that would be:

"Decimal expansion of Euler's first generalized constant."

  • 1
    The problem is that we do not say "Euler's first" but "first Euler" or "first Euler's"... – Iaroslav Mar 18 '15 at 21:56
  • 1
    We start with Euler's constant, which Euler defined. Somebody else then generalizes it to get a generalized Euler's constant. It's not Euler's generalized constant. In mathematics, there's no such thing as a generalized constant. – Peter Shor Mar 19 '15 at 2:14
  • @ Peter Shor My lack of knowledge of mathematics has been revealed. Would it be correct to say, "first generalization of Euler's constant?" – plmadding Mar 19 '15 at 14:32
  • @plmadding I've never seen this wording in math literature. – Vladimir Reshetnikov Mar 19 '15 at 18:37
  • @PeterShor This wording is used sometimes in math papers to refer to indexed Stieltjes constants. "generalized" reflects the fact that the Stieltjes constant with index zero \gamma_0 is just the Euler constant \gamma ... – Vladimir Reshetnikov Mar 19 '15 at 18:44

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