Editing Recurrence relation (section)

===Solving general homogeneous linear recurrence relations===
Many homogeneous linear recurrence relations may be solved by means of the [[generalized hypergeometric series]]. Special cases of these lead to recurrence relations for the [[orthogonal polynomials]], and many [[special function]]s. For example, the solution to

:<math>J_{n+1}=\frac{2n}{z}J_n-J_{n-1}</math>

is given by

:<math>J_n=J_n(z), </math>

the [[Bessel function]], while

:<math>(b-n)M_{n-1} +(2n-b+z)M_n - nM_{n+1}=0 </math>

is solved by

:<math>M_n=M(n,b;z) </math>

the [[confluent hypergeometric series]]. Sequences which are the solutions of [[P-recursive equation|linear difference equations with polynomial coefficients]] are called [[Holonomic function|P-recursive]]. For these specific recurrence equations algorithms are known which find [[Polynomial solutions of P-recursive equations|polynomial]], [[Abramov's algorithm|rational]] or [[Petkovšek's algorithm|hypergeometric]] solutions.