A new class of identities involving Cauchy numbers, harmonic numbers and zeta values

作者：Candelpergher Bernard; Coppo Marc Antoine^*

来源：Ramanujan Journal, 2012, 27(3): 305-328.

DOI：10.1007/s11139-011-9361-7

• Cauchy numbers
• Bell polynomials
• Harmonic numbers
• Laplace-Borel transform
• Mellin transform
• Zeta values
• Ramanujan summation
• Hermite%26apos
• s formula

Improving an old idea of Hermite, we associate to each natural number k a modified zeta function of order k. The evaluation of the values of these functions F (k) at positive integers reveals a wide class of identities linking Cauchy numbers, harmonic numbers and zeta values.

• 出版日期2012-4