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The hockey stick identity confirms, for example: for n=6, r=2: 1+3+6+10+15=35. In combinatorics , the hockey-stick identity , [ 1 ] Christmas stocking identity , [ 2 ] boomerang identity , Fermat's identity or Chu's Theorem , [ 3 ] states that if n ≥ r ≥ 0 {\displaystyle n\geq r\geq 0} are integers, then
The identity is named after Alexandre-Théophile Vandermonde (1772), although it was already known in 1303 by the Chinese mathematician Zhu Shijie. [1] There is a q-analog to this theorem called the q-Vandermonde identity. Vandermonde's identity can be generalized in numerous ways, including to the identity
The proof is similar, but uses the binomial series expansion with negative integer exponents. When j = k, equation gives the hockey-stick identity = = (+ +) ...
The positive part of the identity function: := + ... the shape is widely called a "hockey stick", ... Proof. by the mean of definition 2, it is non-negative in the ...
Proof of Bertrand's postulate; ... Hockey-stick identity; Hyperfactorial; ... Sun's curious identity; Superfactorial; T. Table of Newtonian series;
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Michael Joseph Foy, 33, threw the pole at police and struck officers with the hockey stick as a mob of rioters fought for control of an entrance to the Capitol on Jan. 6, 2021. Foy, a Marine Corps ...
The hockey stick identity follows by equating coefficients of . I came up with this proof, which I think is pretty nice, and I can't find it anywhere else, so I just assume its new. EZ132 ( talk ) 19:09, 18 September 2020 (UTC) [ reply ]