symprod - Product of series

Syntax

Description

symprod(expr) evaluates the product of a series, where expression expr defines the terms of a series, with respect to the default symbolic variable defaultVar determined by symvar. The value of the default variable changes from 1 to defaultVar.

symprod(expr,v) evaluates the product of a series, where expression expr defines the terms of a series, with respect to the symbolic variable v. The value of the variable v changes from 1 to v.

symprod(expr,a,b) evaluates the product of a series, where expression expr defines the terms of a series, with respect to the default symbolic variable defaultVar determined by symvar. The value of the default variable changes from a to b.

symprod(expr,v,a,b) evaluates the product of a series, where expression expr defines the terms of a series, with respect to the symbolic variable v. The value of the variable v changes from a to b.

Tips

• symprod does not compute indefinite products.

Input Arguments

expr	Symbolic expression.
v	Symbolic variable representing the product index.
a	Symbolic number, variable, or expression representing the lower bound of the product index.
b	Symbolic number, variable, or expression representing the upper bound of the product index.

Definitions

Definite Product

The definite product of a series is defined as

Indefinite Product

is called the indefinite product of x_i over i, if the following identity holds for all values of i:

Examples

Evaluate the product of a series for the symbolic expressions k and k^2:

syms k
symprod(k)
symprod((2*k - 1)/k^2)

ans =
factorial(k)
 
ans =
(1/2^(2*k)*2^(k + 1)*factorial(2*k))/(2*factorial(k)^3)

Evaluate the product of a series for these expressions specifying the limits:

syms k
symprod(1 - 1/k^2, k, 2, Inf)
symprod(k^2/(k^2 - 1), k, 2, Inf)

ans =
1/2
 
ans =
2

Evaluate the product of a series for this multivariable expression with respect to k:

syms k x
symprod(exp(k*x)/x, k, 1, 10000)

ans =
exp(50005000*x)/x^10000

See Also

int | syms | symsum | symvar

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