We determine the form and properties of the Weierstrass canonical product of an entire function with real values on ℝ. The proof of the theorem on the order of R-integral is specified [A. M. Samoilenko, “Order and canonical product of the Weierstrass R-integral,” Ukr. Mat. Zh.,71, No. 4, 564–570 (2019)].
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References
K. Weierstrass, Math. Werke, Bd 2, B (1895).
Mathematical Encyclopedia [in Russian], Vol. 2, Sovetskaya Éntsiklopediya, Moscow (1979), pp. 713–714.
J. Hadamard, “’Etude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par Riemann,” J. Math. Pures Appl., 9, Ser. 4, 171–215 (1893).
A. M. Samoilenko, “Order and canonical product of the Weierstrass R-integral,” Ukr. Mat. Zh., 71, No. 4, 564–570 (2019).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 5, pp. 656–662, May, 2019.
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Samoilenko, A.M. Form and Properties of the Canonical Weierstrass Product of an Entire Function with Real Values on ℝ. Ukr Math J 71, 749–757 (2019). https://doi.org/10.1007/s11253-019-01675-y
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DOI: https://doi.org/10.1007/s11253-019-01675-y