What is the paper where the [Liouville theorem](https://en.wikipedia.org/wiki/Harmonic_function#Liouville%27s_theorem) for harmonic function was first stated? Did it come before or after (or in the same paper) as the [Liouville theorem in complex analysis](https://en.wikipedia.org/wiki/Liouville%27s_theorem_(complex_analysis))?



Origin of the Liouville theorem for harmonic functions
References to Liouville go back to his 1847 result that a doubly periodic function without poles is identically constant, which does not yet contain the generalization to either harmonic functions or holomorphic functions.


I quote from [Barry Simon, Harmonic Analysis: A Comprehensive Course in Analysis, Part 3](https://books.google.nl/books?id=YkUACwAAQBAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false) (page 197):



> 
> That any positive harmonic function is constant is due to Bôcher
> (1902), although the theorem is often named after Picard’s rediscovery
> (1923) — there is often reference to the Liouville–Picard theorem.
> 
> 
> 


Bôcher states the theorem in a footnote:


![](https://ilorentz.org/beenakker/MO/Liouville_1.png)
* J. Liouville, [*Leçons
sur les fonctions doublement périodiques*](https://archive.vn/20120711004552/http://gdz.sub.uni-goettingen.de/no_cache/en/dms/load/img/?IDDOC=266004) (1847).
* M. Bôcher, [*Singular
points of functions which satisfy partial differential equations of
the elliptic type*,](https://projecteuclid.org/euclid.bams/1183417472) Bull. Amer. Math. Soc. (2) 9, (1903),
455–465.
* É. Picard, *Deux théorèmes élèmentaires sur les singularités des
fonctions harmoniques*, C. R. Acad. Sci. Paris 176 (1923), 933–935.
