Kramers–Kronig relations

relations connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane
Intangible mathematical_concept Q1424764
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Kramers–Kronig relations

Summary

Kramers–Kronig relations is a mathematical concept[1]. It draws 105 Wikipedia views per month (mathematical_concept category, ranking #154 of 1,007).[2]

Key Facts

  • Kramers–Kronig relations's video is recorded as Kramersgifwiki.gif[3].
  • Kramers–Kronig relations's instance of is recorded as mathematical concept[4].
  • Kramers–Kronig relations's Freebase ID is recorded as /m/07h050[5].
  • Kramers–Kronig relations's defining formula is recorded as \begin{aligned}\Re\chi(\omega)&=\frac1\pi\mathcal P\int_{-\infty}^\infty\frac{\Im\chi(\omega')}{\omega'-\omega}\,\mathrm d\omega '\\Im\chi(\omega)&=-\frac1\pi\mathcal P\int_{-\infty}^\infty\frac{\Re\chi(\omega')}{\omega'-\omega}\,\mathrm d\omega'\end{aligned}[6].
  • Kramers–Kronig relations's Great Russian Encyclopedia Online ID is recorded as 2114286[7].
  • Kramers–Kronig relations's World of Physics ID is recorded as Kronig-KramersRelations[8].
  • Kramers–Kronig relations's schematic is recorded as KramersKronig.svg[9].
  • Kramers–Kronig relations's Microsoft Academic ID is recorded as 196224560[10].
  • Kramers–Kronig relations's OpenAlex ID is recorded as C196224560[11].

Why It Matters

Kramers–Kronig relations draws 105 Wikipedia views per month (mathematical_concept category, ranking #154 of 1,007).[2] It has Wikipedia articles in 16 language editions, a strong signal of global cultural recognition.[12] It is known by 13 alternative names across languages and contexts.[13]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . Freebase Data Dumps. wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [12] . Wikidata sitelinks. wikidata.org.
  3. [13] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Kramers–Kronig relations. Retrieved May 3, 2026, from https://4ort.xyz/entity/kramers-kronig-relations
MLA “Kramers–Kronig relations.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/kramers-kronig-relations.
BibTeX @misc{4ortxyz_kramers-kronig-relations_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Kramers–Kronig relations}}, year = {2026}, url = {https://4ort.xyz/entity/kramers-kronig-relations}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Kramers–Kronig relations — https://4ort.xyz/entity/kramers-kronig-relations (retrieved 2026-05-03)

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