Triple

T6482510
Position Surface form Disambiguated ID Type / Status
Subject Pochhammer symbol E146427 entity
Predicate usedIn P98 FINISHED
Object Gauss hypergeometric function
The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
E596519 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Gauss hypergeometric function | Statement: [Pochhammer symbol, usedIn, Gauss hypergeometric function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gauss hypergeometric function
Context triple: [Pochhammer symbol, usedIn, Gauss hypergeometric function]
  • A. Gamma function
    The Gamma function is a fundamental extension of the factorial function to complex and real non-integer arguments, widely used in analysis, probability, and mathematical physics.
  • B. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • C. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • D. Bessel functions
    Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.
  • E. Jacobi elliptic functions
    Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Gauss hypergeometric function
Triple: [Pochhammer symbol, usedIn, Gauss hypergeometric function]
Generated description
The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gauss hypergeometric function
Target entity description: The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
  • A. Gamma function
    The Gamma function is a fundamental extension of the factorial function to complex and real non-integer arguments, widely used in analysis, probability, and mathematical physics.
  • B. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • C. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • D. Bessel functions
    Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.
  • E. Jacobi elliptic functions
    Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69c0090158c08190af0df9a2348d2d52 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c06a6cd0c4819085a921e6a361d91c completed March 22, 2026, 10:17 p.m.
NED1 Entity disambiguation (via context triple) batch_69c653afb1148190a8683f24a553f64d completed March 27, 2026, 9:53 a.m.
NEDg Description generation batch_69c6559d06c8819082cad37d62fcb3a3 completed March 27, 2026, 10:02 a.m.
NED2 Entity disambiguation (via description) batch_69c6564e01748190a3a12abcc0dfd30f completed March 27, 2026, 10:05 a.m.
Created at: March 22, 2026, 4:51 p.m.