Harmonische Funktion

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Harmonische Funktion

Quality:

Harmonic function - function with vanishing Laplacian. Article “Harmonische Funktion” in German Wikipedia has 8.3 points for quality (as of July 1, 2026). The article contains 0 references and 6 sections. The article also contains templates indicating quality issues, therefore its score was reduced by 0.44 points.

This article has the best quality in English Wikipedia. Also, this article is the most popular in that (German) language version.

In June 2026 the article “Harmonische Funktion” was edited by 1 authors in German Wikipedia and written by 2 authors in all languages.

Since the creation of article “Harmonische Funktion”, its content was written by 47 registered users of German Wikipedia and edited by 517 registered Wikipedia users in all languages.

The article is cited 54 times in German Wikipedia and cited 959 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (German): #25004 in September 2005
  • Global: #8810 in June 2002

The highest popularity rank from 2008:

  • Local (German): #68120 in November 2008
  • Global: #93229 in October 2014

There are 30 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2026 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Harmonic function
36.4272
2French (fr)
Fonction harmonique
32.1047
3Finnish (fi)
Harmoninen funktio
30.9378
4Turkish (tr)
Harmonik fonksiyon
27.9099
5Hungarian (hu)
Harmonikus függvény
26.0208
6Polish (pl)
Funkcja harmoniczna
24.911
7Greek (el)
Αρμονική συνάρτηση
22.0278
8Chinese (zh)
调和函数
21.6744
9Japanese (ja)
調和関数
19.2623
10Spanish (es)
Función armónica
18.5762
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Harmonische Funktion" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Harmonic function
1 707 337
2Spanish (es)
Función armónica
243 580
3Japanese (ja)
調和関数
232 009
4German (de)
Harmonische Funktion
203 536
5Russian (ru)
Гармоническая функция
191 619
6Italian (it)
Funzione armonica
172 006
7French (fr)
Fonction harmonique
138 000
8Chinese (zh)
调和函数
111 604
9Polish (pl)
Funkcja harmoniczna
74 398
10Portuguese (pt)
Função harmônica
73 475
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2026

The most popular language versions of the article "Harmonische Funktion" in June 2026
#LanguagePopularity awardRelative popularity
1English (en)
Harmonic function
3 849
2Russian (ru)
Гармоническая функция
513
3Japanese (ja)
調和関数
497
4German (de)
Harmonische Funktion
332
5Chinese (zh)
调和函数
320
6French (fr)
Fonction harmonique
310
7Spanish (es)
Función armónica
237
8Italian (it)
Funzione armonica
214
9Polish (pl)
Funkcja harmoniczna
170
10Hebrew (he)
פונקציה הרמונית
141
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Harmonische Funktion" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Harmonic function
116
2Italian (it)
Funzione armonica
54
3German (de)
Harmonische Funktion
47
4French (fr)
Fonction harmonique
39
5Japanese (ja)
調和関数
35
6Russian (ru)
Гармоническая функция
34
7Hebrew (he)
פונקציה הרמונית
21
8Dutch (nl)
Harmonische functie
21
9Spanish (es)
Función armónica
18
10Polish (pl)
Funkcja harmoniczna
18
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2026

Language versions of the article "Harmonische Funktion" with the highest AI in June 2026
#LanguageAI awardRelative AI
1German (de)
Harmonische Funktion
1
2Ukrainian (uk)
Гармонічна функція
1
3Arabic (ar)
دالة توافقية
0
4Catalan (ca)
Funció harmònica
0
5Czech (cs)
Harmonická funkce
0
6Greek (el)
Αρμονική συνάρτηση
0
7English (en)
Harmonic function
0
8Esperanto (eo)
Harmonia funkcio
0
9Spanish (es)
Función armónica
0
10Basque (eu)
Funtzio harmoniko
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Harmonische Funktion" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Harmonic function
185
2French (fr)
Fonction harmonique
66
3Polish (pl)
Funkcja harmoniczna
61
4Japanese (ja)
調和関数
58
5German (de)
Harmonische Funktion
54
6Italian (it)
Funzione armonica
54
7Russian (ru)
Гармоническая функция
53
8Spanish (es)
Función armónica
49
9Chinese (zh)
调和函数
47
10Hebrew (he)
פונקציה הרמונית
46
More...

Scores

Estimated value for Wikipedia:
German:
Global:
Popularity in June 2026:
German:
Global:
Popularity in all years:
German:
Global:
Authors in June 2026:
German:
Global:
Registered authors in all years:
German:
Global:
Citations:
German:
Global:

Quality measures

Interwikis

#LanguageValue
arArabic
دالة توافقية
caCatalan
Funció harmònica
csCzech
Harmonická funkce
deGerman
Harmonische Funktion
elGreek
Αρμονική συνάρτηση
enEnglish
Harmonic function
eoEsperanto
Harmonia funkcio
esSpanish
Función armónica
euBasque
Funtzio harmoniko
faPersian
تابع هارمونیک
fiFinnish
Harmoninen funktio
frFrench
Fonction harmonique
heHebrew
פונקציה הרמונית
huHungarian
Harmonikus függvény
itItalian
Funzione armonica
jaJapanese
調和関数
koKorean
조화 함수
nlDutch
Harmonische functie
nnNorwegian (Nynorsk)
Harmonisk funksjon
noNorwegian
Harmonisk funksjon
plPolish
Funkcja harmoniczna
ptPortuguese
Função harmônica
roRomanian
Funcție armonică
ruRussian
Гармоническая функция
slSlovenian
Harmonična funkcija
svSwedish
Harmonisk funktion
trTurkish
Harmonik fonksiyon
ukUkrainian
Гармонічна функція
uzUzbek
Garmonik funksiyalar
zhChinese
调和函数

Popularity rank trends

Best Rank German:
#68120
11.2008
Global:
#93229
10.2014

AI rank trends

Best Rank German:
#25004
09.2005
Global:
#8810
06.2002

Global AI rank history

Languages comparison

Important global interconnections (July 2025 – June 2026)

Wikipedia readers most often find their way to information on Harmonic function from Wikipedia articles about Laplaces equation, Potential theory, Spherical harmonic, Laplace operator and Liouvilles theorem. Whereas reading the article about Harmonic function people most often go to Wikipedia articles on Laplaces equation, Holomorphic function, Spherical harmonic, Simple harmonic motion and Liouvilles theorem.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 16 March 2026

On 16 March 2026 in multilingual Wikipedia, Internet users most often read articles on the following topics: 98th Academy Awards, Michael B. Jordan, Sinners, Jessie Buckley, Paul Thomas Anderson, Sean Penn, One Battle After Another, Amy Madigan, Hamnet, Timothée Chalamet.

In German Wikipedia the most popular articles on that day were: Oscarverleihung 2026, One Battle After Another, Blood & Sinners, Michael B. Jordan, Jessie Buckley, Jürgen Habermas, Sean Penn, Banksy, Liste der größten Auslegerbrücken, Amy Madigan.

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 50 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2026. When calculating current popularity and AI of articles data from June 2026 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2026... More information