Product of series
F = symprod(
returns
the product of the series that expression f
,k
)f
specifies,
which depend on symbolic variable k
. The value
of k
starts at 1
with an unspecified
upper bound. The product F
is returned in terms
of k
where k
represents the
upper bound. This product F
differs from the indefinite
product. If you do not specify k
, symprod
uses
the variable that symvar
determines.
If f
is a constant, then the default variable
is x
.
Find the following products of series
syms k P1 = symprod(1 - 1/k^2, k, 2, Inf) P2 = symprod(k^2/(k^2 - 1), k, 2, Inf)
P1 = 1/2 P2 = 2
Alternatively, specify bounds as a row or column vector.
syms k P1 = symprod(1 - 1/k^2, k, [2 Inf]) P2 = symprod(k^2/(k^2 - 1), k, [2; Inf])
P1 = 1/2 P2 = 2
Find the product of series
syms k x P = symprod(exp(k*x)/x, k, 1, 10000)
P = exp(50005000*x)/x^10000
When you do not specify the bounds of a series
are unspecified, the variable k
starts at 1
.
In the returned expression, k
itself represents
the upper bound.
Find the products of series with an unspecified upper bound
syms k P1 = symprod(k, k) P2 = symprod((2*k - 1)/k^2, k)
P1 = factorial(k) P2 = (1/2^(2*k)*2^(k + 1)*factorial(2*k))/(2*factorial(k)^3)