##  [Fredholm Integral Equation](/fredholm-integral-equation) 

  ##  [Fredholm Integral Equation](https://mathlogic.quantumdictionary.io/fredholm-integral-equation-0) 

  

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Definition

An integral equation in which the integration domain is fixed and independent of the evaluation point, typically written either as ∫_{a}^{b} K(x,y)φ(y) dy = f(x) (first kind) or φ(x) − λ∫_{a}^{b} K(x,y)φ(y) dy = f(x) (second kind), often leading to compact operators on function spaces.