Offset Logarithmic Integral

The offset logarithmic integral, or European logarithmic integral, is a non-elementary function Li(x) differing by a constant from the logarithmic integral function li(x), defined such that:
{\rm Li} (x) = \mathrm{li}(x) - \mathrm{li}(2).\,
Explicitly, this means
{\rm Li} (x) = \int_{2}^{x} \frac{dt}{\ln t} \,
where ln is the natural logarithm. It can be shown that
{\rm Li} (x) = \frac{x}{\ln x} \sum_{k=0}^{\infty} \frac{k!}{(\ln x)^k}
or
\frac{{\rm Li} (x)}{x/\ln x} = 1 + \frac{1}{\ln x} + \frac{2}{(\ln x)^2} + \cdots
It is often used in formulations of the prime number theorem.

 

<< PreviousWord BrowserNext >>
alkaptonuria
czech philharmonic orchestra
city of birmingham symphony orchestra
project xanadu
leu
berlin philharmonic orchestra
the digital village
boston symphony orchestra
john ballance
best first search
william ballantine
robert michael ballantyne
culture of chile
hosea ballou
vmebus
acetylcholine receptor
velvet revolution
jaime luciano balmes
64 bit
henry balnaves
hugh de balsham
computer word
silas deane
charles gravier, comte de vergennes
otto von habsburg
joseph ii, holy roman emperor
joseph i, holy roman emperor
johann heinrich zedler
round island
ice cube
29th century bc
30th century bc
muggles
carlos santana
condorito
condor
bertie ahern
chatterbot
william styron
gottfried keller
blood, sweat & tears
dendritic cell
live '84
loose nut