Curious if this function is called anything.


by hddd123456789
Tags: called, curious, expansion, factorial, function, summation
hddd123456789
hddd123456789 is offline
#1
Dec24-13, 12:09 PM
P: 76
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!
Attached Thumbnails
sum-function.jpg  
Phys.Org News Partner Mathematics news on Phys.org
Math modeling handbook now available
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
hddd123456789
hddd123456789 is offline
#2
Dec24-13, 12:51 PM
P: 76
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.
Pythagorean
Pythagorean is online now
#3
Dec24-13, 01:49 PM
PF Gold
Pythagorean's Avatar
P: 4,212
I don't know, but I think it could be simplified with pi notation:

http://en.wikipedia.org/wiki/Multipl...al_Pi_notation

hddd123456789
hddd123456789 is offline
#4
Dec30-13, 03:08 PM
P: 76

Curious if this function is called anything.


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.
Attached Thumbnails
sum-function.jpg  


Register to reply

Related Discussions
why is the first type bessel function called first? Quantum Physics 1
Integrating a curious function Calculus & Beyond Homework 5
how is it called this function ?? Linear & Abstract Algebra 4
people have actually clicked the part in my sig General Discussion 11
a curious function in quantum gravity Beyond the Standard Model 3