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gfun

  

`rec+rec`

  

termwise sum of two holonomic recurrences

  

`rec*rec`

  

termwise product of two holonomic recurrences

  

cauchyproduct

  

Cauchy product of two holonomic recurrences

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

`rec+rec`(rec1, rec2, u(n))

`rec*rec`(rec1, rec2, u(n))

cauchyproduct(rec1, rec2, u(n))

Parameters

rec1, rec2

-

linear recurrences with polynomial coefficients

u

-

name; recurrence name

n

-

name; index of the recurrence u

Description

• 

The gfun[`rec+rec`](rec1, rec2, u(n)) command returns a termwise sum of two holonomic recurrences, rec1 and rec2.

  

If an and bn are the sequences defined by rec1 and rec2 respectively, the gfun[`rec+rec`] function returns a recurrence for an+bn.

• 

The gfun[`rec*rec`](rec1, rec2, u(n)) command returns a termwise product of two holonomic recurrences, rec1 and rec2.

  

If an and bn are the sequences defined by rec1 and rec2 respectively, the gfun[`rec*rec`] function returns a recurrence for anbn.

• 

The gfun[cauchyproduct](rec1, rec2, u(n)) command returns the Cauchy product of the two holonomic recurrences, rec1 and rec2.

  

If an and bn are the sequences defined by rec1 and rec2 respectively, the gfun[cauchyproduct] function returns a recurrence for their Cauchy product or convolution cn=i=0naibni.

Examples

withgfun:

rec1un+1=n+1un:

rec2un+1=2un:

`rec+rec`rec1,rec2,un

2n2+2nun+n23n+2un+1+n1un+2,u0=_t2+_C0,u1=_t2+2_C0,u2=2_t2+4_C0,u3=6_t2+8_C0

(1)

`rec*rec`rec1,rec2,un

2n2un+un+1

(2)

cauchyproductrec1,rec2,un

2n+4un+4nun+1+un+2,u0=_C0,u1=3_C0

(3)

See Also

gfun

gfun[`diffeq+diffeq`]

gfun[`diffeq*diffeq`]

gfun[hadamardproduct]

gfun[parameters]