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تسجيل

Repeated Integral

المؤلف:  Samko, S. G.; Kilbas, A. A.; and Marichev, O. I.

المصدر:  Fractional Integrals and Derivatives. Yverdon, Switzerland: Gordon and Breach

الجزء والصفحة:  ...

25-8-2018

1795

Repeated Integral

 

A repeated integral is an integral taken multiple times over a single variable (as distinguished from a multiple integral, which consists of a number of integrals taken with respect to different variables). The first fundamental theorem of calculus states that if  is the integral of , then

(1)

Now, if , then

(2)

It follows by induction that if , then the -fold integral of  is given by

			(3)
			(4)

Similarly, if , then

(5)

 

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REFERENCES:

Samko, S. G.; Kilbas, A. A.; and Marichev, O. I. Fractional Integrals and Derivatives. Yverdon, Switzerland: Gordon and Breach, p. 33, 1993.