Difference between revisions of "Exponential integral E"

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=References=
 
=References=
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Exponential integral Ei}}: $5.1.1$
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Exponential integral Ei}}: $5.1.1$ (<i>note: this formula only defines it for $n=1$</i>)
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=findme}}: $5.1.4$
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=findme}}: $5.1.4$ (<i>note:</i> this formula defines it for $n=0,1,2,\ldots$)
  
 
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{{:*-integral functions footer}}
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 00:05, 24 March 2018

The exponential integral functions $E_n$ are defined for $\left|\mathrm{arg \hspace{2pt}}z\right|<\pi$ and $n=1,2,3,\ldots$ by $$E_n(z)=\displaystyle\int_1^{\infty} \dfrac{e^{-zt}}{t^n} \mathrm{d}t.$$

Properties

Relationship between the exponential integral and upper incomplete gamma function
Symmetry relation of exponential integral E
Recurrence relation of exponential integral E

Videos

Laplace transform of exponential integral (2 January 2015)

See Also

Exponential integral Ei

References

$\ast$-integral functions