- #1
Karlisbad
- 131
- 0
If we define the Riemann Integral so:
[tex] \sum_{i=0}^{\infty}f(X_i )(X_{i+1}-X_{i} [/tex]
as a "play" what would happen if i define the integral so:
[tex] \sum_{i=0}^{\infty}f(X_i )(X_{i+1}+X_{i})0.5 [/tex] (2)
In the second definition we define the "mean value" of 2 consecutive points instead of the difference, the question is if 2 is related to the Riemann integral by some formula.
P.D:= Do Bernoulli Polynomials exist in more than 1 dimension?..
[tex] \sum_{i=0}^{\infty}f(X_i )(X_{i+1}-X_{i} [/tex]
as a "play" what would happen if i define the integral so:
[tex] \sum_{i=0}^{\infty}f(X_i )(X_{i+1}+X_{i})0.5 [/tex] (2)
In the second definition we define the "mean value" of 2 consecutive points instead of the difference, the question is if 2 is related to the Riemann integral by some formula.
P.D:= Do Bernoulli Polynomials exist in more than 1 dimension?..