INVESTIGATIONS ON THE EULER-MACLAURIN SUMMATION FORMULA AND ON NUMERICAL SOLUTION OF POLYNOMIAL EQUATIONS.
Final technical rept. 1 Jun 67-31 Mar 69,
BASEL UNIV (SWITZERLAND) MATHEMATICS INST
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A new form for the remainder of the Euler-Maclaurin summation formula is presented, while on the other hand the classical results are generalized in different directions. In particular the results of Jacobi and Malmsten are simplified and improved, introducing the convexity condition. The inequality of G. Gruss, given by him for functions of one variable is generalized to most general spaces, introducing the general linear means of functionals in such spaces. On the other hand new bounds for Gruss expression are derived partly in connection with Tchebicheffs inequality. These bounds depend partly on maximum modulus of the derivative and partly on the integral quadratic mean of the derivative. Author
- Theoretical Mathematics