If 
is regular and of the form 
where 
, for ![R[z]>=0](/images/equations/CarlsonsTheorem/Inline4.svg)
, and if 
for 
, 1, ..., then 
is identically zero.
Carlson's Theorem
See also
Generalized Hypergeometric FunctionExplore with Wolfram|Alpha
References
Bailey, W. N. "Carlson's Theorem." §5.3 in Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 36-40, 1935.Carlson, F. "Sur une classe de séries de Taylor." Dissertation. Uppsala, Sweden, 1914.Hardy, G. H. "On Two Theorems of F. Carlson and S. Wigert." Acta Math. 42, 327-339, 1920.Riesz, M. "Sur le principe de Phragmén-Lindelöf." Proc. Cambridge Philos. Soc. 20, 205-207, 1920.Riesz, M. Erratum to "Sur le principe de Phragmén-Lindelöf." Proc. Cambridge Philos. Soc. 21, 6, 1921.Titchmarsh, E. C. Ch. 5 in The Theory of Functions, 2nd ed. Oxford, England: Oxford University Press, 1960.Wigert, S. "Sur un théorème concernant les fonctions entières." Archiv för Mat. Astr. o Fys. 11, No. 22, 1916.Referenced on Wolfram|Alpha
Carlson's TheoremCite this as:
Weisstein, Eric W. "Carlson's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CarlsonsTheorem.html