summatoryIdentity
P43790
predicate
Indicates that two expressions are identically equal when summed over a specified range, typically expressing an equality between a summation and an equivalent closed-form or alternative summation.
All labels observed (4)
| Label | Occurrences |
|---|---|
| summatoryFunction | 2 |
| summatoryIdentity canonical | 2 |
| sumOverDivisorsIdentity | 1 |
| sumsOver | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: summatoryIdentity
Generated description
Indicates that two expressions are identically equal when summed over a specified range, typically expressing an equality between a summation and an equivalent closed-form or alternative summation.
Sample triples (6)
| Subject | Object |
|---|---|
| Euler’s totient function φ(n) | ∑_{d|n} φ(d) = n ⓘ |
| Euler’s totient function φ(n) | ∑_{d|n} φ(n/d) = n ⓘ |
| Jordan’s totient functions | ∑_{d|n} J_k(d) = n^k via predicate surface "sumOverDivisorsIdentity" ⓘ |
| Liouville function | L(x) = ∑_{n ≤ x} λ(n) via predicate surface "summatoryFunction" ⓘ |
| Möbius function | Mertens function M(n) = ∑_{k≤n} μ(k) via predicate surface "summatoryFunction" ⓘ |
| Lefschetz number | all homological degrees k via predicate surface "sumsOver" ⓘ |