addition formula

The addition formulaPlanetmathPlanetmath of a real ( or complex function shows how the value of the functionMathworldPlanetmath on a sum-formed variable can be expressed with the values of this function and perhaps of another function on 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=j=0n(nj)xn-jyj  (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 formula
Canonical name AdditionFormula
Date of creation 2013-03-22 14:44:20
Last modified on 2013-03-22 14:44:20
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 26
Author pahio (2872)
Entry type Definition
Classification msc 30D05
Classification msc 30A99
Classification msc 26A99
Synonym addition theorem
Defines addition formulae
Defines subtraction formula
Defines subtraction formulae