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Nome (mathematics)

In mathematics, specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions.

Version
v1 · 2026-09-28 · History
Domain-specific #
11000
Domain group
Formal Sciences
Origin domain
Mathematics
Subdomains
Elliptic Functions, Special Functions → Mathematics

Core Idea

Nome (mathematics) is treated here as the recurring cross-domain formal modeling identity summarized by this source-grounded definition: In mathematics, specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions. In mathematics, specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions. This function is of great importance in the description of the elliptic functions, especially in the description of the modular identity of the Jacobi theta function, the Hermite elliptic transcendents and the Weber modular functions, that are used.

Scope of Application

  • Relation to other functionsComplete elliptic integrals. The nome function can be used for the definition of the complete elliptic integrals of first and second kind.

  • Documented setting. This function is of great importance in the description of the elliptic functions, especially in the description of the modular identity of the Jacobi theta function, the Hermite elliptic transcendents and.

  • Applications. where \vartheta{10},\theta{00} are the complete Jacobi theta functions and K(k) is the complete elliptic integral of the first kind with modulus k shown in the formula above.

  • Applications. For the complete theta functions these definitions introduced by Sir Edmund Taylor Whittaker and George Neville Watson are valid.

  • Applications. The nome is commonly used as the starting point for the construction of Lambert series, the q-series and more generally the q-analogs.

Clarity

A clear use of Nome (mathematics) names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In mathematics, specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions.

Manages Complexity

Nome (mathematics) compresses multiple cross-domain formal modeling details into a stable diagnostic relation. The source shows both the central mechanism—these three definition formulas are written down in the fourth edition of the book A Course in Modern Analysis written by Whittaker and Watson on the pages 469 and 470.—and the practical consequence—the following equation follows from these equations by eliminating the complete elliptic integral of the second.

Abstract Reasoning

  1. Type the carrier. Identify the cross-domain formal modeling entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: In mathematics, specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions.
  3. Check operation and conditions. The tiling is referred to as the modular symmetry given by the modular group.
  4. Demand recognition evidence.

Knowledge Transfer

Within the home domain. Knowledge about Nome (mathematics) transfers literally when a new case preserves the same carrier type, relation, and recognition test. The nome function can be used for the definition of the complete elliptic integrals of first and second kind. This function is of great importance in the description of the elliptic functions, especially in the description of the modular identity of the Jacobi theta function, the Hermite elliptic transcendents and the Weber modular functions, that are used for solving equations of higher degrees. Beyond the home domain. No canonical parent is asserted for Nome (mathematics).

Neighborhood in Abstraction Space

Nome (mathematics) sits in a moderately populated region (40th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Continuum Mechanics & Field Models (42 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08