Exponential Integrals

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.