O'zaro farq - Reciprocal difference - Wikipedia Yilda matematika, o'zaro farq a cheklangan ketma-ketlik raqamlar ( x 0 , x 1 , . . . , x n ) { displaystyle (x_ {0}, x_ {1}, ..., x_ {n})} funktsiya haqida f ( x ) { displaystyle f (x)} quyidagi formulalar bilan induktiv tarzda aniqlanadi: r 1 ( x 0 , x 1 ) = x 0 − x 1 f ( x 0 ) − f ( x 1 ) { displaystyle rho _ {1} (x_ {0}, x_ {1}) = { frac {x_ {0} -x_ {1}} {f (x_ {0}) - f (x_ {1}) )}}} r 2 ( x 0 , x 1 , x 2 ) = x 0 − x 2 r 1 ( x 0 , x 1 ) − r 1 ( x 1 , x 2 ) + f ( x 1 ) { displaystyle rho _ {2} (x_ {0}, x_ {1}, x_ {2}) = { frac {x_ {0} -x_ {2}} { rho _ {1} (x_ { 0}, x_ {1}) - rho _ {1} (x_ {1}, x_ {2})}} + f (x_ {1})} r n ( x 0 , x 1 , … , x n ) = x 0 − x n r n − 1 ( x 0 , x 1 , … , x n − 1 ) − r n − 1 ( x 1 , x 2 , … , x n ) + r n − 2 ( x 1 , … , x n − 1 ) { displaystyle rho _ {n} (x_ {0}, x_ {1}, ldots, x_ {n}) = { frac {x_ {0} -x_ {n}} { rho _ {n- 1} (x_ {0}, x_ {1}, ldots, x_ {n-1}) - rho _ {n-1} (x_ {1}, x_ {2}, ldots, x_ {n} )}} + rho _ {n-2} (x_ {1}, ldots, x_ {n-1})}Shuningdek qarang Bo'lingan farqlarAdabiyotlar Vayshteyn, Erik V. "O'zaro farq". MathWorld.Abramovits, Milton; Irene A. Stegun (1972) [1964]. Matematik funktsiyalar bo'yicha qo'llanma (to'qqizinchi Dover bosib chiqarish, o'ninchi GPO bosib chiqarish tahriri). Dover. p.878. ISBN 0-486-61272-4.
funktsiya haqida 
quyidagi formulalar bilan induktiv tarzda aniqlanadi:
