Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Simple Search

Query:
Enter a query and click »Search«...
Format:
Display: entries per page entries
JFM 22.0262.03
Saalschütz, L.
A summation formula. (Eine Summationsformel.)
(German)
[J] Schlömilch Z. XXXV, 186-188 (1890).

Bedeutet $n$ eine ganze positive Zahl, $x,y,v$ beliebige Zahlen, so ist: $$\frac{(x+v+n-1)(x+v+n-2)\dots(x+v)}{(x+n-1)(x+n-2)\dots x}$$ $$-(n)_{1}\ \frac{(x+v+n-1)\dots(x+v+1)}{(x+n-1)\dots(x+1)}\cdot\frac{y+v+n-1}{y}+\cdots$$ $$+(-1)^{n-1}(n)_{n-1}\frac{x+v+n-1}{x+n-1}\ \frac{(y+v+n-1)\dots(y+v+2n-3)}{y\dots(y+n-2)}$$ $$+(-1)^{n}\ \frac{(y+v+n-1)\dots(y+v+2n-2)}{y\dots(y+n-1)}$$ $$=\frac{v(v+1)\dots(v+n-1)(y-x)(y-x+1)\dots(y-x+n-1)}{x(x+1)\dots(x+n-1)y(y+1)\dots(y+n-1)}.$$
(Data of JFM: JFM 22.0262.03; Copyright 2005 Jahrbuch Database used with permission)
[Weltzien, Dr. (Berlin)]
MSC 2000:
*11B75 Combinatorial number theory

Keywords: Summation formula

Highlights
Master Server