Difference between revisions of "Exponential integral Ei"

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(Properties)
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=References=
 
=References=
 
* {{PaperReference|On certain definite integrals involving the exponential-integral|1881|James Whitbread Lee Glaisher|next=Ei(-x)=-Integral from x to infinity of e^(-t)/t dt}}
 
* {{PaperReference|On certain definite integrals involving the exponential-integral|1881|James Whitbread Lee Glaisher|next=Ei(-x)=-Integral from x to infinity of e^(-t)/t dt}}
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Exponential integral E|next=Logarithmic integral}}: $5.1.2$
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Ei(-x)=-Integral from -x to infinity of e^(-t)/t dt|next=Logarithmic integral}}: $5.1.2$
 
 
 
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[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 00:43, 24 March 2018

The exponential integral $\mathrm{Ei}$ is defined for $x>0$ by $$\mathrm{Ei}(x) = \mathrm{PV}\int_{-\infty}^x \dfrac{e^t}{t} \mathrm{d}t,$$ where $\mathrm{PV}$ denotes the Cauchy principal value.


Properties

Ei(-x)=-Integral from -x to infinity of e^(-t)/t dt
Relationship between logarithmic integral and exponential integral
Exponential integral Ei series
Relationship between exponential integral Ei, cosine integral, and sine integral

See Also

Exponential integral E

References

$\ast$-integral functions