In the attached file, the harmonic-like sequence is defined. Is this kind of a sequence known in the literature? Do you know any source with the properties of such numbers?
What do you need to do with this sequence? I would start observing that if you name u(j,r) = 1/j . hj**(r-1), and you form the polynomial (monomial) P(j,r)(X) := u(j,r) X**j. The derivative of this is hj**(r-1) . X**(j-1)
All these monomial polynomials can be summed, the derivation property remains...
There may be differential equationsin physics where you might find these. It seems a fairly common "object" encapsulating classical properties. Anyway using polynomials to expand and then come back and reduce (say X
Thanks for the answer.
I don't need to do anything special, I just want to know if there are any properties of it.
The question comes from obtaining the formula from the attached file (omega function stands for prime omega function in number theory).
I don't get your observation about the derivative though (why did you change notation?). It doesn't really use any property of the sequence h_m^(r). Unless they do, but your anwser wasn't clear enough for me.
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