# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Thu, 8 Dec 2016 03:00:10 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 3 posts ]
 Print view Previous topic | Next topic
Author Message
 Posted: Thu, 18 Mar 2010 05:02:17 UTC
 Senior Member

Joined: Fri, 27 Jan 2006 22:01:08 UTC
Posts: 123
I don't know if I am posting this is the right place, but I am trying to prove the validity of the following formula and was wondering if any of you might
be able to offer me some advice:

where is the Pochhammer symbol for rising factorials used in hypergeometric series, and
, and .
As is indicated by the formula, the sum seems to be independent of and
I have verified this formula using Mathematica for . I have been able to show that this result can be re-written as

where is the Gamma function. I was looking for a proof and I was wondering if you had ever encountered series such as this.
I need this result in order to complete a proof of a Gegenbauer polynomial expansion for powers of the distance between two points in .

Top

 Posted: Thu, 18 Mar 2010 17:14:49 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 7624
Location: NCTS/TPE, Taiwan
howi wrote:
I don't know if I am posting this is the right place, but I am trying to prove the validity of the following formula and was wondering if any of you might
be able to offer me some advice:

where is the Pochhammer symbol for rising factorials used in hypergeometric series, and
, and .
As is indicated by the formula, the sum seems to be independent of and
I have verified this formula using Mathematica for . I have been able to show that this result can be re-written as

where is the Gamma function. I was looking for a proof and I was wondering if you had ever encountered series such as this.
I need this result in order to complete a proof of a Gegenbauer polynomial expansion for powers of the distance between two points in .

Hypergeometric identities? Looks like the methods in book A=B would help you.

_________________

Top

 Posted: Wed, 24 Mar 2010 03:11:29 UTC
 Senior Member

Joined: Fri, 27 Jan 2006 22:01:08 UTC
Posts: 123
outermeasure wrote:
howi wrote:
I don't know if I am posting this is the right place, but I am trying to prove the validity of the following formula and was wondering if any of you might
be able to offer me some advice:

where is the Pochhammer symbol for rising factorials used in hypergeometric series, and
, and .
As is indicated by the formula, the sum seems to be independent of and
I have verified this formula using Mathematica for . I have been able to show that this result can be re-written as

where is the Gamma function. I was looking for a proof and I was wondering if you had ever encountered series such as this.
I need this result in order to complete a proof of a Gegenbauer polynomial expansion for powers of the distance between two points in .

Hypergeometric identities? Looks like the methods in book A=B would help you.

Hi outermeasure. You were absolutely correct. Zeilberger's algorithm directly produces a proof of the identity. Thanks so much for pointing me to these methods.

Its incredible what a computer is capable of. Apparently, the method produces sister identities as well...I am still trying to obtain these, although they are not necessary for my main interest.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 3 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix and Linear Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous