LREtools[HypergeometricTerm] - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Factorization and Solving Equations : LREtools : HypergeometricTerm : LREtools/HypergeometricTerm/IsSolution

LREtools[HypergeometricTerm]

  

IsSolution

  

verify whether an expression is a solution of a linear difference equation depending on a hypergeometric term

  

AreSameSolution

  

verify whether solutions of a linear difference equation depending on a hypergeometric term are equivalent

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IsSolution(sol, r, eq, var)

AreSameSolution(sol, r, sol1, r1, n)

Parameters

sol

-

solution to be checked

r

-

hypergeometric term in the solution sol; specified as a list consisting of the name representing the term in the equation and in the solution and the certificate of the term, such as [t, n+1]

eq

-

difference equation depending on a hypergeometric term

var

-

function variable for which to solve, such as y(x)

sol1

-

solution against which sol is compared

r1

-

hypergeometric term in the solution sol1; specified as a list consisting of the name representing the term in the equation and in the solution and the certificate of the term, such as [t, n+1]

n

-

independent variable

Description

• 

The IsSolution(sol, r, eq, var) command returns true if eq is a linear difference equation with polynomial coefficients depending on a hypergeometric term and sol is its solution. Otherwise, false is returned.

  

The IsSolution function substitutes sol for the function variable and checks the result.

• 

The AreSameSolution(sol, r, sol1, r1, n) command returns true if the solutions sol and sol1 are equivalent. Otherwise, false is returned.

  

The function transforms sol and sol1 to have the same term and checks that the number of linear independent solutions and degrees of corresponding elements in sol and sol1 are the same.

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)

IsSolutionsol,r,eq,yn

true

(3)

sol1t_C1

sol1:=t_C1

(4)

r1t,n

r1:=t,n

(5)

IsSolutionsol1,r1,eq,yn

true

(6)

AreSameSolutionsol1,r1,sol,r,n

true

(7)

eq2nn!+n2zn+12n2nn!+22nn!+n2+2n+1zn

eq:=2nn!+n2zn+12n2nn!+22nn!+n2+2n+1zn

(8)

sol,rPolynomialSolutioneq,zn

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

(9)

IsSolutionsol,r,eq,zn

true

(10)

sol1_C1n2+tnn1n2_C1

sol1:=_C1n2+tnn1n2_C1

(11)

r1t,2n4

r1:=t,2n4

(12)

IsSolutionsol1,r1,eq,zn

true

(13)

AreSameSolutionsol1,r1,sol,r,n

true

(14)

sol2n2+tnn1n2

sol2:=n2+tnn1n2

(15)

IsSolutionsol2,r1,eq,zn

true

(16)

AreSameSolutionsol2,r1,sol,r,n

false

(17)

See Also

LREtools[HypergeometricTerm]

LREtools[HypergeometricTerm][PolynomialSolution]

LREtools[HypergeometricTerm][RationalSolution]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam