expint http://www.openmath.org/CDs/expint.ocd 2003-04-01 2002-01-17 1 0 experimental alg1 arith1 calculus1 cauchypv complex1 fns1 interval1 logic1 nums1 relation1 transc1 This content dictionary contains symbols to describe the Exponential integral and associated functions. Ei The symbol Ei defines the basic exponential integral as in Abramovitz & Stegun equation 5.1.2. This is a Cauchy principal value integral: $$Ei(x)=\int_{-\infty}^x\frac{e^t}t dt\qquad(x>0)$$ which is then extended by analytic continuation (this latter is not currently represented in the FMPs) to the complex plane slit along the negative real axis li The symbol li defines the basic logarithmic integral as in Abramovitz & Stegun equation 5.1.2. This is a Cauchy principal value integral: $$li(x)=\int_0^x\frac1{\ln t}t dt\qquad(x>1)$$ which is then extended by analytic continuation (this latter is not currently represented in the FMPs) to the complex plane slit along the negative real axis E The symbol E defines the generalised exponential integral as in Abramovitz & Stegun equation 5.1.4. This is an ordinary integral: $$E_n(z)=\int_1^{-\infty}\frac{e^{-zt}}{t^n} dt\qquad(\Re z>0)$$ which is then extended by analytic continuation (this latter is not currently represented in the FMPs) to the complex plane slit along the negative real axis. Note that OpenMath's definition is curried, i.e. E(n) is a function. -1