Are there any identities involving this product of Harmonic Numbers?

$$u_{n,m}=\prod_{k=1}^{n-1} H_k \prod_{k=1}^m H_{k+n}$$

My motivation is an attempt to study a series of the form $$\sum_{n=1}^\infty \frac{u_{n,m}}{n^s}x^n$$

Perhaps either the product or sum-of-products has an integral form? Here is an example of an integral form for a sum of a product of two harmonic numbers.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.