It generalizes the factorial function n However, the first formal development of the subject comes in nineteenth century with the contributions of riemann, liouville, grΓΌnwald and letnikov, and since than results have been accumulated in various branches of mathematics. It appears in the method of steepest descent (a method for obtaining the asymptotic expansion of a class of integrals).
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Later, euler notices that due to his gamma function derivatives and integrals of fractional orders may have a meaning
