Curious if this function is called anything.

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Discussion Overview

The discussion revolves around a function derived from factorial expansion, with participants exploring its properties and whether it has a recognized name. The scope includes theoretical exploration and mathematical reasoning.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant introduces a function related to factorial expansion and seeks information about its name and properties.
  • Another participant points out a correction regarding the notation used in the function, specifically the indices.
  • A different participant suggests that the function could potentially be expressed using pi notation, referencing a related mathematical concept.
  • One participant identifies the function as (unsigned) Stirling numbers of the first kind, noting the relationship between the parameters 'a' and 'n' and providing a revised version of the function.

Areas of Agreement / Disagreement

The discussion includes multiple viewpoints regarding the nature of the function, with no consensus on its established name or properties. Some participants propose different interpretations and corrections without resolving the overall question.

Contextual Notes

Participants express uncertainty about the function's properties and its relationship to known mathematical concepts, indicating a need for further clarification on definitions and assumptions.

hddd123456789
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Hey everyone, I was just playing around with factorial expansion and after grouping some terms I noticed a pattern for which I made a function. I am happy to provide more details as needed, but for now I have attached an image of the function and am curious, as per the title, whether this is known and if so if it has a name and/or interesting properties. I forgot to put this on the image but I was only considering positive naturals for a and n when defining the function.

Thanks!
 

Attachments

  • sum-function.jpg
    sum-function.jpg
    10.5 KB · Views: 580
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Sorry, I should've posted this after working out the kinks. The a-n-1, a-n-2 part should be a-(n-1), a-(n-2), ... and k_n=n-1 should be k_n=n.
 
Last edited:
Actually, I figured out that these are (unsigned) Stirling numbers of the first kind (save where n=0), with 'a' being the rows of its pyramid, and 'n' being the column in each row. Ironic that I called the function S. I attached a simpler (and more accurate) version for anyone interested.
 

Attachments

  • sum-function.jpg
    sum-function.jpg
    7.1 KB · Views: 549
Last edited:

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