NOTE ON CAHEN′S INTEGRAL FORMULAS
2002
We present an explicit form for a class of definite integrals whose special cases include some definite integrals evaluated, over a century ago, by Cahen who made use of an appropriate contour integral for the integrand of a well-known integral representation of the Riemann Zeta function given in (3). Furthermore another analogous class of definite integral formulas and some identities involving Riemann Zeta function and Euler numbers En are also obtained as by-products.
Keywords:
- Calculus
- Mathematics
- Particular values of Riemann zeta function
- Mathematical analysis
- Exponential integral
- Multiple integral
- Arithmetic zeta function
- Prime-counting function
- Riemann Xi function
- Riemann integral
- Proof of the Euler product formula for the Riemann zeta function
- Riemann hypothesis
- Riemann–Stieltjes integral
- Improper integral
- Correction
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