Ramanujan-Soldner constant

Function graph from left

The Ramanujan-Soldner constant is a mathematical constant that is defined as the only positive zero of the logarithm li. It is named after S. Ramanujan and Johann Georg von Soldner , but was examined by Lorenzo Mascheroni as early as 1792 .

The infinite decimal fraction begins with

${\displaystyle \mu =1{,}45136\ 92348\ 83381\ 05028\ 39684\ 85892\ 02744\ 94930\ 32283\ 64801\ \dots }$(Follow A070769 in OEIS )

There are 75,500 decimal places known (as of August 2010).

literature

• Lorenzo Mascheroni : Adnotationes ad calculum integralem Euleri / In quibus nonnulla Problemata from Eulero proposita resolvuntur / Pars altera . Petrus Galeatius, Ticini 1792 (Latin; "z = 1.45137" on p. 17 )
• Johann Georg Soldner : Théorie et tables d'une nouvelle fonction transcendante , Lindauer, Munich 1809 (French; "li. 1.4513692346 = 0" on p. 42 )

Web links

• Eric W. Weisstein : Soldner's Constant . In: MathWorld (English).
• Follow A099803 in OEIS ( continued fraction expansion of μ)

Individual evidence

1. ↑ Constants and Records of Computation by Xavier Gourdon and Pascal Sebah, August 12, 2010 (English)