Difference between revisions of "Exponential integral Ei"

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The exponential integral $\mathrm{Ei}$ is defined for $x>0$ by
 
The exponential integral $\mathrm{Ei}$ is defined for $x>0$ by
$$\mathrm{Ei}(x) = \int_{-\infty}^x \dfrac{e^t}{t} \mathrm{d}t.$$
+
$$\mathrm{Ei}(x) = \mathrm{PV}\int_{-\infty}^x \dfrac{e^t}{t} \mathrm{d}t,$$
 +
where $\mathrm{PV}$ denotes the [[Cauchy principal value]] and $e^t$ denotes the [[exponential]].
  
  
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=Properties=
 
=Properties=
[[Exponential integral with negative exponent on e in definition]]<br />
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[[Ei(-x)=-Integral from -x to infinity of e^(-t)/t dt]]<br />
 
[[Relationship between logarithmic integral and exponential integral]]<br />
 
[[Relationship between logarithmic integral and exponential integral]]<br />
 
[[Exponential integral Ei series]]<br />
 
[[Exponential integral Ei series]]<br />
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=References=
 
=References=
* {{PaperReference|On certain definite integrals involving the exponential-integral|1881|James Whitbread Lee Glaisher|next=findme}}
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* {{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}}: $5.1.2$
+
* {{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}}: $5.1.2$
 
 
 
{{:*-integral functions footer}}
 
{{:*-integral functions footer}}
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 00:48, 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 and $e^t$ denotes the exponential.


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