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A group representation of a group G on a vector space V can be restricted to a subgroup H. For example, the symmetric group on three letters has a representation phi on R^2 ...

The Hall-Montgomery constant is related to the multiplicative spectrum of completely multiplicative functions and has closed form delta_0 = ...

The symbol defined by (v,n) = (2^(-2n){(4v^2-1)(4v^2-3^2)...[4v^2-(2n-1)^2]})/(n!) (1) = ((-1)^ncos(piv)Gamma(1/2+n-v)Gamma(1/2+n+v))/(pin!), (2) where Gamma(z) is the gamma ...

Let X be a metric space, A be a subset of X, and d a number >=0. The d-dimensional Hausdorff measure of A, H^d(A), is the infimum of positive numbers y such that for every ...

A polygonal number of the form n(5n-3)/2. The first few are 1, 7, 18, 34, 55, 81, 112, ... (OEIS A000566). The generating function for the heptagonal numbers is ...

A pyramidal number of the form n(n+1)(5n-2)/6, The first few are 1, 8, 26, 60, 115, ... (OEIS A002413). The generating function for the heptagonal pyramidal numbers is ...

The heptanacci constant is the limiting ratio of adjacent heptanacci numbers. It is the algebraic number P = (x^7-x^6-x^5-x^4-x^3-x^2-x-1)_1 (1) = 1.99196419660... (2) (OEIS ...

A figurate number which is equal to the cubic number n^3. The first few are 1, 8, 27, 64, ... (OEIS A000578).

A pyramidal number of the form n(n+1)(4n-1)/6, The first few are 1, 7, 22, 50, 95, ... (OEIS A002412). The generating function of the hexagonal pyramidal numbers is ...

The hexanacci constant is the limiting ratio of adjacent hexanacci numbers. It is the algebraic number P = (x^6-x^5-x^4-x^3-x^2-x-1)_2 (1) = 1.98358284342... (2) (OEIS ...