E637 -- Nova demonstratio, quod evolutio potestatum binomii Newtoniana etiam pro exponentibus fractis valeat
(A new demonstration, with respect to which prevails the expansion of binomial powers by Newton even by fractional exponents)
Here Euler notes the recursive relation for the general binomial coefficients, that if
(1 + x)a =
Sn = 0∞a
n xn and if
(a + x)a + 1 =
Sn = 0∞
then bn = an +
an - 1, generalizing the usual recursive relationship for the binomial coefficients.
Presented to the Academy on May 20, 1776.
Originally published in Nova Acta Academiae Scientarum Imperialis Petropolitinae 5, 1789, pp. 52-58
- Opera Omnia: Series 1, Volume 16, pp. 112 - 121
- Original publication: E637
- German translation (Artur Diener and Alexander Aycock): E637
- The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E637 include:
- Dhombres J., “Some aspects of the history of functional-equations linked to the evolution of the function concept.” Archive for History of Exact Sciences, 36 (2), pp. 91-181 (1986).
- Dhombres J, Pensivy M., “Rigor and mathematical presentations in the 18th-century - the example of proof by aepinus.” Historia Mathematica, 15 (1), pp. 9-31 (Feb 1988).
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