recursion formula: meaning, definition, pronunciation and examples
LowFormal Technical
Quick answer
What does “recursion formula” mean?
A rule that defines each term in a sequence based on the previous term(s).
Audio
Pronunciation
Definition
Meaning and Definition
A rule that defines each term in a sequence based on the previous term(s).
In mathematics and computer science, a formula or algorithm that expresses successive elements of a sequence or structure in terms of preceding ones, often used to define sequences, fractals, or computational functions.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage. The spelling 'formula' remains constant, with 'formulae' as an alternative plural in both varieties.
Connotations
Technical, precise, mathematical. Connotes logical progression and defined steps.
Frequency
Equally low-frequency and specialised in both British and American English, confined to academic and technical contexts.
Grammar
How to Use “recursion formula” in a Sentence
[subject] + [verb] + recursion formula + [for/in] + [sequence/function]Vocabulary
Collocations
Usage
Meaning in Context
Business
Almost never used.
Academic
Primary context. Used in mathematics, computer science, and engineering papers to define sequences or algorithms.
Everyday
Never used.
Technical
Standard term in programming (e.g., defining factorial) and advanced mathematics.
Vocabulary
Synonyms of “recursion formula”
Strong
Neutral
Weak
Vocabulary
Antonyms of “recursion formula”
Watch out
Common Mistakes When Using “recursion formula”
- Confusing 'recursion formula' with 'recursive function' (the latter is a broader implementation).
- Using 'recursive formula' as a spelling variant (less standard).
- Mispronouncing 'recursion' as 're-curse-ion'.
FAQ
Frequently Asked Questions
Yes, in most mathematical contexts, they are synonyms, though 'recurrence relation' is slightly more formal and general.
Primarily in university-level mathematics, computer science courses (especially algorithm design), and technical programming documentation.
Yes, many recursion formulas require a set of initial values (base cases) to begin the iterative calculation.
An explicit or closed-form formula, which calculates any term directly without referencing previous terms.
A rule that defines each term in a sequence based on the previous term(s).
Recursion formula is usually formal technical in register.
Recursion formula: in British English it is pronounced /rɪˈkɜː.ʒən ˈfɔː.mjʊ.lə/, and in American English it is pronounced /rɪˈkɝː.ʒən ˈfɔːr.mjə.lə/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of a set of Russian nesting dolls: each doll contains a smaller version of itself, just as a recursion formula defines the next item based on the current one.
Conceptual Metaphor
DEFINITION AS A CHAIN OF STEPS; A SEQUENCE AS A LADDER WHERE EACH RUNG DEPENDS ON THE ONE BELOW.
Practice
Quiz
What is a 'recursion formula' primarily used for?