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LREtools[HypergeometricTerm]

  

SubstituteTerm

  

return solution with a directly substituted hypergeometric term instead of a name representing it in the solution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

SubstituteTerm(sol, term, n)

Parameters

sol

-

rational function in n and a name representing a hypergeometric term

term

-

hypergeometric term

n

-

independent variable

Description

• 

The SubstituteTerm(sol, term, n) returns the solution with a directly substituted hypergeometric term instead of a name representing it in the solution.

• 

The hypergeometric term in the linear difference equation is specified by a name, for example, t. The meaning of the term is defined by the parameter term. The term is specified as a list consisting of the name of the term variable and the consecutive term ratio, for example, t,n+1.

• 

The solution is the function, corresponding to n. The solution involves arbitrary constants of the form, for example, _c1 and _c2.

Examples

withLREtoolsHypergeometricTerm:

eqyn+2n!+nyn+1+nn!1yn

eq:=yn+2n!+nyn+1+nn!1yn

(1)

sol,rPolynomialSolutioneq,yn

sol,r:=t_C1n,t,n+1

(2)

SubstituteTermsol,r,n

Γn_C1

(3)

eqt+n2zn+12nt+2t+n2+2n+1zn

eq:=n2+tzn+1n2+2nt+2n+2t+1zn

(4)

sol,rPolynomialSolutioneq,zn,t=2nn!

sol,r:=n2_C1+t_C1,t,2n+2

(5)

SubstituteTermsol,r,n

_C12nΓn+1+n2

(6)

References

  

Bronstein, M. "On solutions of Linear Ordinary Difference Equations in their Coefficients Field." INRIA Research Report. No. 3797. November 1999.

See Also

LREtools[HypergeometricTerm]

LREtools[HypergeometricTerm][PolynomialSolution]

LREtools[HypergeometricTerm][RationalSolution]

 


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