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searching for Summation notation 32 found (34 total)

Einstein notation (2,074 words) [view diff] exact match in snippet view article find links to article

notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed

Two-point tensor (647 words) [view diff] exact match in snippet view article find links to article

Piola–Kirchhoff stress tensor. As with many applications of tensors, Einstein summation notation is frequently used. To clarify this notation, capital indices are

1/2 + 1/4 + 1/8 + 1/16 + ⋯ (856 words) [view diff] exact match in snippet view article find links to article

series that converges absolutely. The sum of the series is 1. In summation notation, this may be expressed as 1 2 + 1 4 + 1 8 + 1 16 + ⋯ = ∑ n = 1 ∞ (

Feynman slash notation (945 words) [view diff] exact match in snippet view article find links to article

^{2}A_{2}+\gamma ^{3}A_{3}} where γ are the gamma matrices. Using the Einstein summation notation, the expression is simply A / = d e f γ μ A μ {\displaystyle {A\

Mercator series (945 words) [view diff] exact match in snippet view article find links to article

\ln(1+x)=x-{\frac {x^{2}}{2}}+{\frac {x^{3}}{3}}-{\frac {x^{4}}{4}}+\cdots } In summation notation, ln ⁡ ( 1 + x ) = ∑ n = 1 ∞ ( − 1 ) n + 1 n x n . {\displaystyle \ln(1+x)=\sum

Gross–Neveu model (1,097 words) [view diff] exact match in snippet view article find links to article

}}_{a}\ \psi ^{a}\right]^{2}\ ,} where the formula uses Einstein summation notation. Each wave function ψ a {\displaystyle \ \psi ^{a}\ } is a two

Series (mathematics) (12,839 words) [view diff] exact match in snippet view article

{\displaystyle a_{1}+a_{2}+a_{3}+\cdots ,} or, using capital-sigma summation notation, ∑ i = 1 ∞ a i . {\displaystyle \sum _{i=1}^{\infty }a_{i}.} The infinite

Summation (4,582 words) [view diff] exact match in snippet view article find links to article

empty sum. These degenerate cases are usually only used when the summation notation gives a degenerate result in a special case. For example, if n = m

Leibniz formula for determinants (2,127 words) [view diff] exact match in snippet view article find links to article

in terms of the Levi-Civita symbol and makes use of the Einstein summation notation, where it becomes det ( A ) = ϵ i 1 ⋯ i n a 1 i 1 ⋯ a n i n , {\displaystyle

1 − 2 + 3 − 4 + ⋯ (3,577 words) [view diff] exact match in snippet view article find links to article

successive positive integers, given alternating signs. Using sigma summation notation the sum of the first m terms of the series can be expressed as ∑ n

Eigenfunction (2,347 words) [view diff] exact match in snippet view article find links to article

\end{aligned}}} This is the matrix multiplication Ab = c written in summation notation and is a matrix equivalent of the operator D acting upon the function

Kabsch algorithm (1,138 words) [view diff] exact match in snippet view article find links to article

notation, H = P T Q {\displaystyle H=P^{\mathsf {T}}Q\,} or, using summation notation, H i j = ∑ k = 1 N P k i Q k j , {\displaystyle H_{ij}=\sum _{k=1}^{N}P_{ki}Q_{kj}

OptimJ (1,709 words) [view diff] exact match in snippet view article find links to article

i in 1 .. 10}; This construction is very similar to the big-sigma summation notation used in mathematics, with a syntax compatible with the Java language

Killing form (1,865 words) [view diff] exact match in snippet view article find links to article

e_{k}]]=[e_{i},{c_{jk}}^{m}e_{m}]={c_{im}}^{n}{c_{jk}}^{m}e_{n}} in Einstein summation notation, where the cijk are the structure coefficients of the Lie algebra

99 Bottles of Beer (1,354 words) [view diff] exact match in snippet view article find links to article

geometric progressions, differentials, Euler's identity, complex numbers, summation notation, the Cantor set, the Fibonacci sequence, and the continuum hypothesis

Pushforward (differential) (2,483 words) [view diff] exact match in snippet view article

}}^{b}}{\partial u^{a}}}{\frac {\partial }{\partial v^{b}}},} in the Einstein summation notation, where the partial derivatives are evaluated at the point in U {\displaystyle

Constant scalar curvature Kähler metric (1,043 words) [view diff] exact match in snippet view article find links to article

associated to the Kähler form, and summation here is taken with Einstein summation notation. The vector space of holomorphy potentials, denoted by h {\displaystyle

Geometric calculus (3,338 words) [view diff] exact match in snippet view article find links to article

_{i}:F\mapsto (x\mapsto (\nabla _{e_{i}}F)(x)).} Then, using the Einstein summation notation, consider the operator: e i ∂ i , {\displaystyle e^{i}\partial _{i}

Elastic energy (1,927 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \varepsilon _{ij}} is the strain tensor (Einstein summation notation has been used to imply summation over repeated indices). The values

Stress–energy tensor (4,040 words) [view diff] exact match in snippet view article find links to article

variables (not exponents; see Tensor index notation and Einstein summation notation). If Cartesian coordinates in SI units are used, then the components

Standard deviation (8,233 words) [view diff] exact match in snippet view article find links to article

discussion on Bessel's correction further down below. or, by using summation notation, σ = 1 N ∑ i = 1 N ( x i − μ ) 2 , where μ ≡ 1 N ∑ i =

Binomial theorem (6,735 words) [view diff] exact match in snippet view article find links to article

referred to as the binomial formula or the binomial identity. Using summation notation, it can be written more concisely as ( x + y ) n = ∑ k = 0 n ( n k

Polynomial (8,173 words) [view diff] exact match in snippet view article find links to article

polynomial function. This can be expressed more concisely by using summation notation: ∑ k = 0 n a k x k {\displaystyle \sum _{k=0}^{n}a_{k}x^{k}} That

Cauchy–Schwarz inequality (5,175 words) [view diff] exact match in snippet view article find links to article

{u_{2}^{2}}{v_{2}}}+\cdots +{\frac {u_{n}^{2}}{v_{n}}},} or, using summation notation, ( ∑ i = 1 n u i ) 2 / ∑ i = 1 n v i ≤ ∑ i = 1 n u i 2 v i . {\displaystyle

Gradient (5,701 words) [view diff] exact match in snippet view article find links to article

x^{j}}}\mathbf {e} _{i}\otimes \mathbf {e} _{k},} (where the Einstein summation notation is used and the tensor product of the vectors ei and ek is a dyadic

Curvature (6,492 words) [view diff] exact match in snippet view article find links to article

normal N, the shape operator can be expressed compactly in index summation notation as ∂ a N = − S b a X b . {\displaystyle \partial _{a}\mathbf {N} =-S_{ba}\mathbf

Mathematics (15,928 words) [view diff] exact match in snippet view article find links to article

An explanation of the sigma (Σ) summation notation

The Vectors of Mind (1,996 words) [view diff] exact match in snippet view article find links to article

multiplication, diagonal matrices, the inverse, the characteristic equation, summation notation, linear dependence, geometric interpretations, orthogonal transformations

Mathematical economics (10,736 words) [view diff] exact match in snippet view article find links to article

different from modern notation but can be constructed using more modern summation notation. Walras assumed that in equilibrium, all money would be spent on all

Simple continued fraction (9,622 words) [view diff] exact match in snippet view article find links to article

\over a_{4}}.} Carl Friedrich Gauss used a notation reminiscent of summation notation, x = a 0 + K 4 i = 1 1 a i , {\displaystyle x=a_{0}+{\underset {i=1}{\overset

Musical isomorphism (5,000 words) [view diff] exact match in snippet view article find links to article

locally in terms of this coframe as g = gij ei ⊗ ej using Einstein summation notation. Given a vector field X = Xi ei and denoting gij Xi = Xj, its flat

Two-state quantum system (6,603 words) [view diff] exact match in snippet view article find links to article

{\boldsymbol {\sigma }}\cdot \mathbf {B} \psi } , it can be written in summation notation after some rearrangement as ∂ ψ ∂ t = i μ ℏ σ i B i ψ {\displaystyle