Two different functions of real argument are called this way:
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which are related to each other as:
{\rm Ei}(x) = - E_1(-x) |
There is a trend to moving from definition (which was dominating in the past) towards which becomes more and more popular nowdays.
Fig. 1. A sample graph of |
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where ... is Euler–Mascheroni constant | ||||
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The real-value positive function of two real-value positive arguments (time and radial coordinate ):
{\rm w}(t, r) = E_1 \left( \frac{r^2}{4 t} \right) = -{\rm Ei} \left( - \frac{r^2}{4 t} \right) |
honours a planar axial-symmetric diffusion equation with homogenous initial and boundary conditions:
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and is widely used in radial heat-mass transfer analysis.