Convolution formulae for Bernoulli numbers

  title={Convolution formulae for Bernoulli numbers},
  author={Wenchang Chu and Chenying Wang},
By computing higher derivatives of hyperbolic cotangent function, we investigate convolutions of Bernoulli numbers. Several general summation formulae are derived, extending a few well-known ones, for example those due to Euler and Rademacher [Topics in Analytic Number Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1973].