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There is a trend to moving from
definition which was dominating in the past towards
.
Approximations
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| LaTeX Math Block |
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| {\rm Ei}(x) = \gamma + \ln |x| + \sum_{k=1}^\infty \frac{x^k}{k\cdot k!} |
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| LaTeX Math Block |
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| {\rm Ei}(x) = e^x \, \left[ \frac{1}{x} + \sum_{k=2}^\infty \frac{(k-1)!}{x^k} \right] |
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| LaTeX Math Block |
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| {\rm Ei}(-x) \sim \gamma + \ln x |
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| LaTeX Math Block |
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| {\rm Ei}(x) \sim \gamma + \ln x |
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Application
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The function
| LaTeX Math Inline |
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| body | \displaystyle f(t, r) = {\rm Ei} \left( - \frac{r^2}{4 \, t} \right) |
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honor the axial symmetric diffusion equation: | LaTeX Math Block |
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\frac{\partial f}{\partial t} = \frac{\partial f^2}{\partial^2 r} + \frac{1}{r} \frac{\partial f}{\partial r} |
References
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https://www.wolframalpha.com/input/?i=Ei(x)
