Carlson's Theorem

If f(z) is regular and of the form O(e^(k|z|)) where k<pi, for R[z]>=0, and if f(z)=0 for z=0, 1, ..., then f(z) is identically zero.

See also

Generalized Hypergeometric Function

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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.

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Carlson's Theorem

Cite this as:

Weisstein, Eric W. "Carlson's Theorem." From MathWorld--A Wolfram Web Resource.

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