The essence of the generalized Newton binomial theorem |
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| Institution: | 1. Department of Mathematics, University of Tampa, 401 West Kennedy Blvd., Campus Box 2928, Tampa, FL 33606, USA;2. Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611, USA;3. Department of Mathematics, West Chester University, PA 19383, USA;4. Institute of Mathematics, P.O. Box 1-764, Bucharest, Romania;1. School of Mathematics and System Sciences & LMIB, BeiHang University, Beijing 100191, PR China;2. Advanced Mathematical Institute, Osaka City University, 558-8585, Japan;1. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China;2. College of Sciences, North China University of Technology, Beijing 100144, PR China;3. Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, PR China;1. Departamento de Matemáticas, Universidad Católica del Norte (UCN), Avenida Angamos 0610, Antofagasta, CP 1270709, Chile;2. Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso (PUCV), Blanco Viel 596, Cerro Barón, Valparaíso, CP 2350026, Chile;1. School of Mathematics and System Sciences, LMIB, BeiHang University, Beijing 100191, PR China;2. Advanced Mathematical Institute, Osaka City University, 558-8585, Japan |
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| Abstract: | Under the frame of the homotopy analysis method, Liao gives a generalized Newton binomial theorem and thinks it as a rational base of his theory. In the paper, we prove that the generalized Newton binomial theorem is essentially the usual Newton binomial expansion at another point. Our result uncovers the essence of generalized Newton binomial theorem as a key of the homotopy analysis method. |
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