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
`rec+rec`(rec1, rec2, u(n))
`rec*rec`(rec1, rec2, u(n))
cauchyproduct(rec1, rec2, u(n))
rec1, rec2
-
linear recurrences with polynomial coefficients
u
name; recurrence name
n
name; index of the recurrence u
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=0naibn−i.
withgfun:
rec1≔un+1=n+1un:
rec2≔un+1=2un:
`rec+rec`rec1,rec2,un
2n2+2nun+−n2−3n+2un+1+n−1un+2,u0=_t2+_C0,u1=_t2+2_C0,u2=2_t2+4_C0,u3=6_t2+8_C0
`rec*rec`rec1,rec2,un
−2n−2un+un+1
cauchyproductrec1,rec2,un
2n+4un+−4−nun+1+un+2,u0=_C0,u1=3_C0
See Also
gfun[`diffeq+diffeq`]
gfun[`diffeq*diffeq`]
gfun[hadamardproduct]
gfun[parameters]
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