Functions > Symbolic Functions > Exponential Integrals
Exponential Integrals
Ei(x)—Returns the exponential integral function (Cauchy principal value) of x, which is defined as follows:
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Ei(x) returns only the real part of the complex exponential integral function.
For x > 0, the integral is interpreted as the Cauchy principal value.
Ei(n, x)—Returns the generalized exponential integral function of x.
For an arbitrary integer n, Ei(n, x) is defined by the recurrence relation:
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For the case of n = 1, Ei(n, x) is defined as follows:
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where γ is Euler's constant.
For a real number x, Ei(x) and Ei(n, x) are related to each other as follows:
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Arguments
x is a real scalar, a vector, or a square matrix. When using the generalized exponential integral function, x can also be complex scalar.
n is a real or complex scalar.
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