In mathematics, the classical Kronecker limit formula describes the constant term at s = 1 of a real analytic Eisenstein series (or Epstein zeta function)...

Kronecker are the Kronecker limit formula, Kronecker's congruence, Kronecker delta, Kronecker comb, Kronecker symbol, Kronecker product, Kronecker's method...

(\tau )}}|\eta (\tau )|^{2}\right)} can be evaluated using the Kronecker limit formula. Here χ is the quadratic residue symbol modulo D, where −D is the...

{1}{n}}.} introduced by Zagier (1975) who used it to obtain a Kronecker limit formula for real quadratic fields. Masri, Riad (2004), "The Herglotz–Zagier...

website. Chowla–Selberg formula Ramanujan–Sato series q-series Weierstrass's elliptic functions Partition function Kronecker limit formula Affine Lie algebra...

{\displaystyle n} , and δ m , n {\displaystyle \delta _{m,n}} is the Kronecker delta. If the weight function w ( x ) {\displaystyle w(x)} satisfies the...

zeta-function. The constant term of the pole at s = 1 is described by the Kronecker limit formula. The modified function E ∗ ( z , s ) = π − s Γ ( s ) ζ ( 2 s )...

two-dimensional torus. This case is named Kronecker foliation, after Leopold Kronecker and his Kronecker's Density Theorem. If the real number θ is distinct...

}{\partial x^{i_{k}}}}\right)={\frac {1}{k!}}.} Alternatively, an explicit formula can be given for the exterior derivative of a k-form ω, when paired with...

{\displaystyle C_{\lambda [n],\mu [n],\nu [n]}} reaches its limit. The reduced Kronecker coefficients are structure constants of Deligne categories of...

called the delta function because it is a continuous analogue of the Kronecker delta function, which is usually defined on a discrete domain and takes...

orthonormal Cartesian coordinate system, the metric tensor is just the kronecker delta δ i j {\displaystyle \delta _{ij}} or δ i j {\displaystyle \delta...

mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols...

Slepian, David (1972), "On the symmetrized Kronecker power of a matrix and extensions of Mehler's formula for Hermite polynomials", SIAM Journal on Mathematical...

fraction, KG Ramanathan - Acta Arith, 1984 Some applications of Kronecker’s limit formula, KG Ramanathan - J. Indian Math. Soc, 1987 Mahbubani, Kishore...

the relativistic velocity addition formula, the relativistic Doppler effect, relativistic mass, a universal speed limit, mass–energy equivalence, the speed...

{p}}_{j}]=i\hbar \delta _{ij},} where δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. This relation is attributed to Werner Heisenberg, Max Born and...

m=0,1,2...} and δ denotes the Kronecker delta. Solving for B m ∓ {\displaystyle B_{m}^{\mp {}}} gives the recursive formulas B m − = δ m , 0 − ∑ k = 0 m...

_{\omega (n)\Omega (n)}\lambda (n),} where δ {\displaystyle \delta } is the Kronecker delta, λ ( n ) {\displaystyle \lambda (n)} is the Liouville function,...

analysis. Limit of a sequence Subsequential limit – the limit of some subsequence Limit of a function (see List of limits for a list of limits of common...

Zhang, Liang-Cheng (6 June 1997). "Ramanujan's class invariants, Kronecker's limit formula, and modular equations". Transactions of the American Mathematical...

Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory...

he proved the first class number formula for quadratic forms (later refined by his student Kronecker). The formula, which Jacobi called a result "touching...

respect to P (and its own natural filtration), where δij denotes the Kronecker delta. The spectral content of a stochastic process X t {\displaystyle...

that the successor function generates all natural numbers. Also, Leopold Kronecker said "God made the integers, all else is the work of man". This may be...

j−, and j2 denote operators. The δ {\displaystyle \delta } symbols are Kronecker deltas. We now consider systems with two physically different angular...

{R} _{R})} where ⊗ {\displaystyle \otimes } denotes the Kronecker product. Under the Kronecker model, the spatial correlation depends directly on the eigenvalue...

{\displaystyle \sum _{j}\chi ^{j}(\beta )(2j+1)=\delta (\beta ).} The set of Kronecker product matrices D j ( α , β , γ ) ⊗ D j ′ ( α , β , γ ) {\displaystyle...

{\displaystyle a=d_{0}(-d_{1})^{-5/4}} . This form is required by the Hermite–Kronecker–Brioschi method, Glasser's method, and the Cockle–Harley method of differential...

}{\text{tr}}[e^{-\rho t}d\rho e^{-\rho t}d\rho ]\ dt,} or in terms of Kronecker product and vectorization, [ D B ( ρ , ρ + d ρ ) ] 2 = 1 2 vec [ d ρ ]...