Joseph Knar

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

${\displaystyle \Gamma (1+x)=2^{2x}\prod _{n=1}^{\infty }{\frac {\Gamma ({\frac {1}{2}}+2^{-n}x)}{\sqrt {\pi }}}}$

for ${\displaystyle x>0}$.[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)

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