1. Joined
    06 Mar '12
    Moves
    625
    29 Sep '15 15:529 edits
    I want to name a maths function because I will often mention it in my book I am writing but don't know what I should call it. I am using this function within certain discrete probability mass functions that use a special unique mathematical model which I have named the "progressive successor model of probability" and which only can work with a discrete variable which is a count of a series of events where each event may or may not have a successor -not sure if any of that info helps here.

    I am aware of what is conventionally called the Riemann zeta function ζ(s) which outputs a list of mathematical constants where:

    ζ(1) = ∑ [X = 1, ∞] 1 / ( X^1)
    ζ(2) = ∑ [X = 1, ∞] 1 / ( X^2)
    ζ(3) = ∑ [X = 1, ∞] 1 / ( X^3)
    ...etc

    but what I want to know is if there is a conventional name for the similar function (or mathematical series ), which I will symbolize with f() just temporarily for now, which outputs a list of mathematical constants but where:

    f(1) = ∑ [X = 1, ∞] 1 / (( X^1) (X + 1))
    f(2) = ∑ [X = 1, ∞] 1 / (( X^2) (X + 1))
    f(3) = ∑ [X = 1, ∞] 1 / (( X^3) (X + 1))
    ...etc.

    ?

    and, if there is no such conventionally name for the above function then do any of you here, who generally know more about mathematics than I do, have any suggestions of what I could appropriately call it and what notation or letter or symbol I could appropriately use in my book to represent it?

    + Would it be exactly correct to call that function a "harmonic series" in my book or is it not quite literally a "harmonic series"?
    I don't want to call it harmonic if that isn't strictly correct.
  2. Standard memberDeepThought
    Losing the Thread
    Cosmopolis
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    29 Sep '15 16:47
    Originally posted by humy
    I want to name a maths function because I will often mention it in my book I am writing but don't know what I should call it. I am using this function within certain discrete probability mass functions.

    I am aware of what is conventionally called the Riemann zeta function ζ(s) which outputs a list of mathematical constants where:

    ζ(1) = ∑ [X = 1, ∞] 1 ...[text shortened]... literally a "harmonic series"?
    I don't want to call it harmonic if that isn't strictly correct.
    Your function looks like it can be rewritten as a Dirichlet series, in which case this Wikipedia page might be of interest:

    https://en.wikipedia.org/wiki/Dirichlet_series
  3. Joined
    06 Mar '12
    Moves
    625
    30 Sep '15 07:19
    Originally posted by DeepThought
    Your function looks like it can be rewritten as a Dirichlet series, in which case this Wikipedia page might be of interest:

    https://en.wikipedia.org/wiki/Dirichlet_series
    Thanks for that. I will mull over it. Some of that maths looks very difficult.