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- Title
THE USE OF COMPLEX FUNCTIONS IN THE STUDY OF EULER'S INTEGRALS Γ AND β.
- Authors
Lixandru, Ion
- Abstract
Two of the most important properties of Euler's Γ and β integrals are presented in this article using the theory of complex functions: the complements formula, the formula of connection between Γ and β, as well as applications of these formulas. The theorem of residues for a certain complex function and an integrated contour conveniently chosen, different variable changes, as well as the change of the order of integration in a double integral were used for this purpose. Three alternative demonstrations are presented for the formula of connection between Γ and β, the last of them using the Laplace transform. At the end of the article two practical applications are presented: one belonging to Raabe, the other using the Laplace transform.
- Subjects
EULER'S numbers; LAPLACE transformation; RESIDUE theorem; IMPROPER integrals; MATHEMATICAL variables
- Publication
Annals of the University Dunarea de Jos of Galati: Fascicle II, Mathematics, Physics, Theoretical Mechanics, 2011, Vol 34, Issue 2, p336
- ISSN
2067-2071
- Publication type
Article