Chu–Vandermonde identity
(0.001 seconds)
11—20 of 144 matching pages
11: 22.9 Cyclic Identities
§22.9 Cyclic Identities
… ►§22.9(ii) Typical Identities of Rank 2
… ► ►§22.9(iii) Typical Identities of Rank 3
… ►12: Bibliography T
13: 24.5 Recurrence Relations
§24.5(ii) Other Identities
… ►§24.5(iii) Inversion Formulas
►In each of (24.5.9) and (24.5.10) the first identity implies the second one and vice-versa. …14: 15.17 Mathematical Applications
§15.17(iv) Combinatorics
►In combinatorics, hypergeometric identities classify single sums of products of binomial coefficients. …15: 27.15 Chinese Remainder Theorem
16: 17.17 Physical Applications
17: 17.18 Methods of Computation
18: 35.10 Methods of Computation
19: David M. Bressoud
20: Errata
The upper-index of the finite sum which originally was , was replaced with since .
Reported by Gergő Nemes on 2021-08-23
In Equation (1.13.4), the determinant form of the two-argument Wronskian
was added as an equality. In ¶Wronskian (in §1.13(i)), immediately below Equation (1.13.4), a sentence was added indicating that in general the -argument Wronskian is given by , where . Immediately below Equation (1.13.4), a sentence was added giving the definition of the -argument Wronskian. It is explained just above (1.13.5) that this equation is often referred to as Abel’s identity. Immediately below Equation (1.13.5), a sentence was added explaining how it generalizes for th-order differential equations. A reference to Ince (1926, §5.2) was added.
The overloaded operator is now more clearly separated (and linked) to two distinct cases: equivalence by definition (in §§1.4(ii), 1.4(v), 2.7(i), 2.10(iv), 3.1(i), 3.1(iv), 4.18, 9.18(ii), 9.18(vi), 9.18(vi), 18.2(iv), 20.2(iii), 20.7(vi), 23.20(ii), 25.10(i), 26.15, 31.17(i)); and modular equivalence (in §§24.10(i), 24.10(ii), 24.10(iii), 24.10(iv), 24.15(iii), 24.19(ii), 26.14(i), 26.21, 27.2(i), 27.8, 27.9, 27.11, 27.12, 27.14(v), 27.14(vi), 27.15, 27.16, 27.19).
Three new identities for Pochhammer’s symbol (5.2.6)–(5.2.8) have been added at the end of this subsection.
Suggested by Tom Koornwinder.
Originally the second occurrence of the function was given incorrectly as .
Reported 2014-05-21 by Hanyou Chu.