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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
Download QR code; Print/export ... This is a list of q-analogs in mathematics and related fields. Algebra. Iwahori–Hecke algebra ... q-Vandermonde identity ...
As with the (non-q) Chu–Vandermonde identity, there are several possible proofs of the q-Vandermonde identity. The following proof uses the q -binomial theorem . One standard proof of the Chu–Vandermonde identity is to expand the product ( 1 + x ) m ( 1 + x ) n {\displaystyle (1+x)^{m}(1+x)^{n}} in two different ways.
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Vandermonde's identity This page was last ...
Lagrange's identity; Lagrange's trigonometric identities; List of logarithmic identities; MacWilliams identity; Matrix determinant lemma; Newton's identity; Parseval's identity; Pfister's sixteen-square identity; Sherman–Morrison formula; Sophie Germain identity; Sun's curious identity; Sylvester's determinant identity; Vandermonde's identity ...
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. There are two lists of mathematical identities related to ...
Another way to derive the above formula is by taking a limit of the Vandermonde matrix as the 's approach each other. For example, to get the case of x 1 = x 2 {\displaystyle x_{1}=x_{2}} , take subtract the first row from second in the original Vandermonde matrix, and let x 2 → x 1 {\displaystyle x_{2}\to x_{1}} : this yields the ...
We can avoid writing large exponents for using the fact that for any exponent we have the identity =. This is the Vandermonde matrix for the roots of unity, up to the normalization factor. Note that the normalization factor in front of the sum ( 1 / N {\displaystyle 1/{\sqrt {N}}} ) and the sign of the exponent in ω are merely conventions, and ...