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
1532
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
Similarly, if 
, then
 |
(5)
|
REFERENCES:
Samko, S. G.; Kilbas, A. A.; and Marichev, O. I. Fractional Integrals and Derivatives. Yverdon, Switzerland: Gordon and Breach, p. 33, 1993.
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