Cauchy formula for repeated integration [SEP] named after
Cauchy formula for repeated integration
The Cauchy formula for repeated integration, named after Augustin Louis Cauchy, allows one to compress "n" antidifferentiations of a function into a single integral (cf. Cauchy's formula).
Scalar case.
Let "ƒ" be a continuous function on the real line. Then the "n"th repeated integral of "ƒ" based at "a",
is given by single integration
A proof is given by induction. Since "ƒ" is continuous, the base case
–Euler equation
- Cauchy functional equation
- Cauchy formula for repeated integration
- Cauchy–Frobenius lemma
- Cauchy–Hadamard theorem
- Cauchy horizon
- Cauchy's integral formula
- Cauchy's integral theorem
- Cauchy interlacing theorem
- Cauchy–Kovalevskaya theorem
- Cauchy matrix
- Cauchy momentum equation
- Cauchy net
- Cauchy number
- Cauchy–Peano theorem
- Cauchy principal value
- Cauchy problem
- Cauchy product
- Cauchy's radical test
- Cauchy–