# Why can't I find anyone who has discovered the (irrational) constant 1.29128…? [closed]

The constant is exactly $\sum_{n=1}^∞\frac{1}{n^n}$. Why does it seem that no one has written about it? Did I not search well enough? If so, what is the name for it? If not, it is not sufficiently "interesting?" I can't find it anywhere, which seems very strange.

(I apologize about how little my experience in higher maths I have...)

## closed as unclear what you're asking by user223391, Adam Hughes, JonMark Perry, Marc van Leeuwen, SchrodingersCatJun 1 '16 at 9:28

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• See the sophomore's dream – Omnomnomnom May 31 '16 at 21:04
• @MiloBrandt: yes it is. Due to Lagrange inversion theorem, such a constant is related with the Lambert function. If such a constant were rational, it would give $e^a=b$ with $a,b\in\mathbb{Q}$. That may happen only at $a=0$ since $e$ is a trascendental number. – Jack D'Aurizio May 31 '16 at 21:04
• The OEIS has a page about it: oeis.org/A073009. You can find it by typing in the digits 1, 2, 9, 1, 2, 8 into the search bar. Also see the references in the "Links" section on that page. – Rahul May 31 '16 at 21:06
• But obviously its "weirdness" is not enough to prove its irrationality. – Jack D'Aurizio May 31 '16 at 21:06
• @asherdrummond Erm... how do you do the logical jump between the first and second part of your sentence? – Clement C. May 31 '16 at 21:24

What? You mean the Sophomore's Dream? (Actually, the "dream" is that $\int_0^1 x^{-x} \,\mathrm{d}x = \sum_{n=1}^\infty n^{-n}$, but this is just two representations of your value.)
• Why do you think it has "a name" other than "the constant $\sum_{n=1}^\infty n^{-n}$"? That's a short and unambiguous identifier. – Eric Towers May 31 '16 at 23:19