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Taylor Series & Taylor Polynomials definitions

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  • Sequence
    An ordered list of numbers generated by a specific formula, where each entry corresponds to a particular value of an index.
  • Term
    A single entry in an ordered list, calculated by substituting a specific index value into a given formula.
  • Index
    A variable, often denoted by n, that identifies the position of an entry within an ordered list.
  • Factorial
    A product of all positive integers up to a given number, with zero yielding a value of one by definition.
  • Zero Factorial
    A special case in products of consecutive integers, defined to have a value of one.
  • Formula
    A mathematical expression used to generate each entry in an ordered list based on the index.
  • Substitution
    The process of replacing a variable in an expression with a specific value to compute a result.
  • Product
    A result obtained by multiplying two or more numbers or expressions together.
  • Square
    A value obtained by multiplying a number by itself, often seen in expressions like n squared.
  • Calculation
    A step-by-step process of simplifying expressions to obtain numerical results for each entry.
  • Expression
    A combination of numbers, variables, and operations that represents a mathematical relationship.
  • Natural Number
    A positive integer used as an index in ordered lists, typically starting from one.
  • Ordered List
    A collection of numbers arranged in a specific sequence, each associated with a unique position.
  • Pattern
    A recognizable regularity in the arrangement or values of entries within an ordered list.
  • Simplification
    The process of reducing a mathematical expression to its most basic numerical form.