AngouriMath
Product(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity)
Method (no overloads)
Summary
A product of expr as var runs from
from to to inclusive. Mirrors
Sum(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity), with an empty range multiplying to
1 .
Sum(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity), with an empty range multiplying to
Parameter "expr"
The factor. It may mention var .
Parameter "var"
The index, which this binds.
Parameter "from"
The first value of the index.
Parameter "to"
The last value of the index, inclusive.
Returns
The product written out where the bounds are concrete integers and there are not too
many terms; a closed form where the factor is a monomial in the index — a
narrower class than the sum's, a product having no linearity to take a sum of terms
apart with; and an unevaluated node otherwise.
many terms; a closed form where the factor is a monomial in the index — a
narrower class than the sum's, a product having no linearity to take a sum of terms
apart with; and an unevaluated node otherwise.
Remarks
The closed form's condition is to >= from rather than the sum's
to >= from - 1 : at the empty range itself it would be c ^ 0 , which is
undefined atc = 0 where the empty product is 1 . Where the index is in
the factor the lower bound must be a concrete integer of at least one, since the
answer is a ratio of factorials andfactorial has no value at the negative
integers.
undefined at
the factor the lower bound must be a concrete integer of at least one, since the
answer is a ratio of factorials and
integers.
Example
using System;
using AngouriMath;
using static AngouriMath.MathS;
Console.WriteLine(Product("k", "k", 1, 5).Simplify());Prints
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