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" State & Prove Dirichlet Theorem For Triple Integrals "​

Answer 1

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If we consider the integral I=∫∞0e−tta−1dt , it is once seen to be an infinite and improper integral. This integral is infinite because the upper limit of integration is infinite and it is improper because t=0 is a point of infinite discontinuity of the integrand, if a<1 , where a is either real number or real part of a complex number. This integral is known as Euler’s Integral. This is of a great importance in mathematical analysis and calculus. The result, i.e., integral, is defined as a new function of real number a , as Γ(a)=∫∞0e−tta−1dt .