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Gamma, Beta, Erf > SinIntegral[z] > Introduction to the exponential integrals

Definitions of exponential integrals

The exponential integral , exponential integral , logarithmic integral , sine integral , hyperbolic sine integral , cosine integral , and hyperbolic cosine integral are defined as the following definite integrals, including the Euler gamma constant :

The previous integrals are all interrelated and are called exponential integrals.

Instead of the above classical definitions through definite integrals, equivalent definitions through infinite series can be used, for example, the exponential integral can be defined by the following formula (see the following sections for the corresponding series for the other integrals):