borel transform meaning in Hindi

Examples

1. The integral form for the generalized Borel transform follows as well.
2. Nachbin's theorem gives necessary and sufficient conditions for the Borel transform to be well defined.
3. The generalized Borel transform allows a different weighting function to be used, rather than the exponential function, to transform functions not of exponential type.
4. In particular, Nachbin's theorem may be used to give the domain of convergence of the "'generalized Borel transform "', given below.
5. Suppose that the Borel transform converges for all real numbers to a function growing sufficiently slowly that the following integral is well defined ( as an improper integral ), the "'Borel sum "'of " A " is given by
6. More precisely, the series for the Borel transform converges in a neighborhood of the origin, and can be analytically continued to the positive real axis, and the integral defining the Borel sum converges to " f " ( " z " ) for " z " in the region above.