An application of difference calculus. (Q1550908)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: An application of difference calculus. |
scientific article; zbMATH DE number 2709525
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An application of difference calculus. |
scientific article; zbMATH DE number 2709525 |
Statements
An application of difference calculus. (English)
0 references
1879
0 references
In diesem Aufsatze wird die Summation der Reihe \[ S_m=a^m+(a+1)^mx^1+(a+2)^mx^2+(a+3)^mx^3+\cdots \] wo \(x\) ein echter Bruch ist, vorgenommen. Man erhält \[ S_m=\frac{C_0+C_1x+C_2x^2+\cdots +C_mx^m}{(1-x)^{m+1}}\,, \] wo \[ \begin{aligned} C_0 & = a^m,\quad C_1=(a+1)^m-(m+1)_1a^m,\\ C_2 & = (a+2)^m-(m+1)_1(a+1)^m+(m+1)_2a^m,\cdots.\end{aligned} \]
0 references
finite difference
0 references
series expansion
0 references
