• Introduction
• Iteration
  • Summation
  • Product
  • Set Notation
  • Nested Iteration
  • Conditions on indices
  • Union and Intersection
  • General Iteration
• General Symbols
  • Cases
  • Function Composition
  • Set Containment
  • Kronecker
• Operations
  • Factorial
  • Binomial
• Differentiation
  • Derivative
  • Partial Derivative
  • Gradient

Product $\prod$

The product symbol $\prod$ specifies a product of multiple terms. The symbol is a capital greek letter "Pi", so Pi for product.

Basic form $\prod\limits_{i=0}^n f_i$ or $\prod_{i=0}^n f_i$

Parts:

• $i=0$: Name of the index with initial value
• $n$: Last value of the named index. ATTENTION! The last index is inclusive, so $i$ will take on that value and not stop one before that
• $f_i$: The $i$-th product term. This could be any expression using (or not using!) $i$

Meaning: Multiply each term $f_i$, starting at $i=0$ and ending at $i=n$. If the upper stop value is lower than the initial value, then the sum is $1$, e.g. $\prod\limits_{i=1}^0 = 1$.

Code: