Joseph Knar Explained

Joseph Knar
Birth Date:	1 January 1800
Nationality:	Austrian
Alma Mater:	University of Graz
Occupation:	Mathematician
Known For:	Knar's formula

Joseph Knar (January 1, 1800 – June 1, 1864) was an Austrian mathematician working at the University of Graz.^[1] He is most well known for discovering Knar's formula, an infinite product formula involving the gamma function.

Life

From a poor family, Knar graduated from the University of Graz at the age of 19 after studying mathematics and law. In 1821, he became a full professor, a position which he held until his death from a stroke in 1864. He published several books including a two-volume textbook Lehrbuch der Elementarmathematik on elementary mathematics.

Knar's Formula

Knar's most famous mathematical contribution was his discovery of the infinite product formula

\Gamma( 1+ x) = 2 ^{2x} \prod ^{inf ty} _{n =1} (\Gamma( (1)/(+2 ^{-n} x) 2))/(\sqrt{\pi) }for x > 0 .^[2]

Publications

• Neues, sehr einfaches Verfahren zur Ausziehung der Wurzeln aus bestimmten Zahlen (1824)
• Lehrbuch der Elementarmathematik, 2 volumes (1828–1829)
• Theorie der harmonischen Reihen in Archiv der Mathematik und Physik (1864)

Notes and References

1. S. Gunther, Joseph Knar, Allgemeine Deutsche Biographie 16 (1882) 269.
2. J. Knar, Die harmonischen reihen, Archiv der Mathematik und Physik 41–42 (1864) p. 360