In mathematics, an addition theorem is a formula such as that for the exponential function: ex + y = ex · ey, that expresses, for a particular function...

and periodicity above). These are also known as the angle addition and subtraction theorems (or formulae). sin ⁡ ( α + β ) = sin ⁡ α cos ⁡ β + cos ⁡ α...

{\displaystyle (2\ell +1)} . Many facts about spherical harmonics (such as the addition theorem) that are proved laboriously using the methods of analysis acquire...

modularity theorem. This is an important theorem in number theory. It was part of Andrew Wiles' proof (1995) of Fermat's Last Theorem. The addition theorem states...

existence of this instantaneous axis is guaranteed by the Euler's rotation theorem). All points on a rigid body experience the same angular velocity at all...

immediately generalized Fagnano's results and posed his algebraic addition theorem for elliptic integrals. Except for a comment by Landen his ideas were...

Addition (usually signified by the plus symbol, +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

ISBN 978-0-444-86126-9. MR 0634800. Henry Mann (1976), Addition Theorems: The Addition Theorems of Group Theory and Number Theory (Corrected reprint of...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

\end{aligned}}} The Jacobi epsilon and zn functions satisfy a quasi-addition theorem: E ( x + y , m ) = E ( x , m ) + E ( y , m ) − m sn ⁡ ( x , m ) sn...

theorem (proof theory) Deduction theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem...

ISBN 978-0-8218-4351-2. Zbl 1124.11003. Mann, Henry (1976). Addition Theorems: The Addition Theorems of Group Theory and Number Theory (Corrected reprint of...

mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses...

Cauchy proved the spectral theorem for symmetric matrices, i.e., that every real, symmetric matrix is diagonalizable. In addition, Cauchy was the first to...

arithmetic of abelian varieties. The tangent-chord process (one form of addition theorem on a cubic curve) had been known as far back as the seventeenth century...

Number Theory. George Allen & Unwin. Mann, Henry B. (1976). Addition Theorems: The Addition Theorems of Group Theory and Number Theory (Corrected reprint of...

Freiman's theorem. Restricted sumset Sidon set Sum-free set Schnirelmann density Shapley–Folkman lemma X + Y sorting Henry Mann (1976). Addition Theorems: The...

The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate...

Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing...

The incomplete elliptic integral of the first kind has following addition theorem[citation needed]: F [ arctan ⁡ ( x ) , k ] + F [ arctan ⁡ ( y ) , k...

ЛИТЕРАТУРЫ. Translated as Gradshtein, I. S. (1963). Direct and Converse Theorems: The Elements of Symbolic Logic. Translated by Boddington, T. Oxford, London...

In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample...

Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving...

where θ is the spherical polar angle of r. With the spherical-harmonic addition theorem the equation can be rewritten as e i k ⋅ r = 4 π ∑ ℓ = 0 ∞ ∑ m = −...

-\mu }}^{1/2}{\binom {2\ell +2\lambda +1}{2\lambda }}^{-1/2}.} The addition theorems were proved in different manners by several authors. The regular solid...

Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used...

number theory Nathanson (1996) II:1 Henry Mann (1976). Addition Theorems: The Addition Theorems of Group Theory and Number Theory (Corrected reprint of...

multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem from...

known as Abel elliptic functions. They can be continued using the addition theorems. For example adding ± 1 2 ω {\displaystyle \pm {\tfrac {1}{2}}\omega...