addition formulas

The addition formulaPlanetmathPlanetmath of a real ( or complex function shows how the value of the functionMathworldPlanetmath at a sum-formed variable can be expressed with the values of this function and perhaps of another function at the addends.


  1. 1.

    Addition formula of an additive functionMathworldPlanetmath f,

  2. 2.

    Addition formula of the natural power function, i.e. the binomial theoremMathworldPlanetmath,
    (x+y)n=ν=0n(nν)xνyn-ν  (n=0, 1, 2,)

  3. 3.

    Addition formula of the exponential functionDlmfDlmfMathworldPlanetmath (,

  4. 4.

    Addition formulae of the trigonometric functionsDlmfMathworldPlanetmath (, e.g.
    cos(x+y)=cosxcosy-sinxsiny,11The addition formula of cosine is sometimes called “the mother of all formulae”.tan(x+y)=tanx+tany1-tanxtany

  5. 5.

    Addition formulae of the hyperbolic functionsDlmfMathworldPlanetmath, e.g.

  6. 6.

    Addition formula of the Bessel functionDlmfMathworldPlanetmathPlanetmath,
    Jn(x+y)=ν=-Jν(x)Jn-ν(y)  (n=0,±1,±2,)

The five first of those are instances of ; e.g. coshx  and  sinhx  are tied together by the algebraic connection (  cosh2x-sinh2x=1.

One may also speak of the subtraction formulae of functions — one example would be  ex-y=exey.

Title addition formulas
Canonical name AdditionFormulas
Date of creation 2013-03-22 19:35:28
Last modified on 2013-03-22 19:35:28
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 6
Author pahio (2872)
Entry type Definition
Classification msc 30D05
Classification msc 30A99
Classification msc 26A99
Related topic ExampleOnSolvingAFunctionalEquation
Related topic ProofOfAdditionFormulaOfExp
Related topic AdditionFormulasForSineAndCosine
Related topic AdditionFormulaForTangent
Related topic AdditionAndSubtractionFormulasForHyperbolicFunctions
Defines addition formula
Defines subtraction formula