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# ExpIntegralE

 ExpIntegralE[n, z]gives the exponential integral function En(z).
• Mathematical function, suitable for both symbolic and numerical manipulation.
• .
• ExpIntegralE[n, z] has a branch cut discontinuity in the complex z plane running from - to 0.
• For certain special arguments, ExpIntegralE automatically evaluates to exact values.
• ExpIntegralE can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Series for generic and logarithmic cases:
Evaluate numerically:
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Series for generic and logarithmic cases:
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 Scope   (2)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex arguments:
Infinite arguments give exact results:
ExpIntegralE threads element-wise over lists and arrays:
ExpIntegralE can be applied to power series:
Series expansion at infinity:
Give the result for an arbitrary symbolic direction:
 Applications   (3)
Plot over the complex plane:
Solution of the heat equation for piecewise-constant initial conditions:
Check that the solution satisfies the heat equation:
Plot the solution for different times:
Calculate a classic asymptotic series:
Plot the difference of a truncated series and the exponential integral sum:
Use FullSimplify to simplify exponential integrals:
Use FunctionExpand to express special cases in simpler functions:
Numerically find a root of a transcendental equation:
Generate from integrals, sums, and differential equations:
ExpIntegralE appears as special cases of hypergeometric functions:
Integrals:
ExpIntegralE is a numeric function:
Large arguments can give results too large to be computed explicitly:
Machine-number inputs can give high-precision results:
In TraditionalForm, is not automatically interpreted as an exponential integral:
Plot the Riemann surface of :
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