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HEUN FUNCTION

  • Heun function
  • Function for Heun's differential equation

    the local Heun function H ℓ ( a , q ; α , β , γ , δ ; z ) {\displaystyle H\ell (a,q;\alpha ,\beta ,\gamma ,\delta ;z)} is the solution of Heun's differential

    Heun function

    Heun_function

  • Karl Heun
  • German mathematician (1859–1929)

    German mathematician who introduced Heun's equation, Heun functions, and Heun's method. Karl Heun studied mathematics and philosophy at the University of

    Karl Heun

    Karl Heun

    Karl_Heun

  • Heun's method
  • Procedure for solving ODEs

    In mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule),

    Heun's method

    Heun's_method

  • Holonomic function
  • Type of functions, in mathematical analysis

    class of hypergeometric functions. Examples of special functions that are holonomic but not hypergeometric include the Heun functions. Examples of holonomic

    Holonomic function

    Holonomic_function

  • List of eponyms of special functions
  • Hermann Hankel: Hankel function Heine: Heine functions Charles Hermite: Hermite polynomials Karl L. W. M. Heun (1859 – 1929): Heun's equation J. Horn: Horn

    List of eponyms of special functions

    List_of_eponyms_of_special_functions

  • Lamé function
  • Solutions of Lamé's equation

    } which after a change of variable becomes a special case of Heun's equation. A more general form of Lamé's equation is the ellipsoidal equation

    Lamé function

    Lamé_function

  • Predictor–corrector method
  • Algorithms in numerical analysis

    method for the corrector step. A simple predictor–corrector method (known as Heun's method) can be constructed from the Euler method (an explicit method) and

    Predictor–corrector method

    Predictor–corrector_method

  • Bateman Manuscript Project
  • and elliptic and theta functions Equations of mathematical physics, including continuous and discrete Painlevé, Lamé and Heun equations Transforms and

    Bateman Manuscript Project

    Bateman_Manuscript_Project

  • Diffusion model
  • Technique for the generative modeling of a continuous probability distribution

    any of the numerical integration methods, such as Euler–Maruyama method, Heun's method, linear multistep methods, etc. Just as in the discrete case, one

    Diffusion model

    Diffusion_model

  • Burning Sun scandal
  • 2019 South Korean media sex scandal

    from the original on March 28, 2019. Retrieved March 20, 2019. Kim, Jae-heun (March 10, 2019). "Big Bang's Seungri booked on sex bribery charge". The

    Burning Sun scandal

    Burning Sun scandal

    Burning_Sun_scandal

  • Regular singular point
  • Concept in differential equation mathematics

    A solution is the hypergeometric function. Arscott, F. M. (1995). "Heun's Equation". In Ronveaux, A. (ed.). Heun's Differential Equations. Oxford University

    Regular singular point

    Regular_singular_point

  • Min Hee-jin
  • South Korean art director (born 1979)

    Archived from the original on May 17, 2024. Retrieved May 18, 2024. Kim, Jae-heun (May 13, 2024). "Ador CEO's fate to be decided on May 17". The Korea Herald

    Min Hee-jin

    Min Hee-jin

    Min_Hee-jin

  • Runge–Kutta methods
  • Family of implicit and explicit iterative methods

    {1}{2}}} gives the midpoint method, α = 1 {\displaystyle \alpha =1} is Heun's method, and α = 2 3 {\displaystyle \alpha ={\tfrac {2}{3}}} is Ralston's

    Runge–Kutta methods

    Runge–Kutta methods

    Runge–Kutta_methods

  • List of Runge–Kutta methods
  • {\displaystyle {\begin{array}{c|cc}0&0&0\\1/2&1/2&0\\\hline &0&1\\\end{array}}} Heun's method is a second-order method with two stages. It is also known as the

    List of Runge–Kutta methods

    List_of_Runge–Kutta_methods

  • Korea Tourism Organization
  • Government agency of South Korea

    Bulletin. "한국관광공사: 역대 CEO". knto.or.kr (in Korean). Retrieved 2025-09-30. Jae-heun, Kim (2025-07-24). "Actor Park Bo-gum new face of Korea's tourism". The Korea

    Korea Tourism Organization

    Korea Tourism Organization

    Korea_Tourism_Organization

  • Stroad
  • Type of thoroughfare

    p. 254. Slaughter 2021, 3:04. Slaughter 2021, 6:00. Van Antwerp, Jeremy; Heun, Matthew Kuperus (2022). A Framework for Sustainability Thinking: A Student's

    Stroad

    Stroad

    Stroad

  • List of laboratory biosecurity incidents
  • Failures to secure dangerous animals and pathogens

    Retrieved 2025-09-20. Lee, Changhwan; Jang, Eun Jung; Kwon, Donghyok; Choi, Heun; Park, Jung Wan; Bae, Geun-Ryang (7 April 2016). "Laboratory-acquired dengue

    List of laboratory biosecurity incidents

    List_of_laboratory_biosecurity_incidents

  • Ligand-gated ion channel
  • Type of ion channel transmembrane protein

    galantamine, rivastigmine and memantine (review): final appraisal determination Heun R, Corral RM, Ahokas A, Nicolini H, Teixeira JM, Dehelean P (2013). "1643

    Ligand-gated ion channel

    Ligand-gated ion channel

    Ligand-gated_ion_channel

  • Demis Hassabis
  • British AI researcher (born 1976)

    Archived from the original on 2 July 2022. Retrieved 11 June 2020. Kahng, Jee Heun (15 March 2016). "Google artificial intelligence program beats S. Korean

    Demis Hassabis

    Demis Hassabis

    Demis_Hassabis

  • List of 2026 albums
  • Drops New Album Same Difference". Clash. Retrieved April 4, 2026. Kim, Jae-heun (March 20, 2026). "T.O.P returns with first solo studio album on April 3"

    List of 2026 albums

    List_of_2026_albums

  • KAIST
  • South Korean public research university

    improvement. Kyoungchul Kong, Mechanical engineer, entrepreneur and academic Heun Lee, identified mechanism behind hydrogen storage in ice particles Ji-O Lee

    KAIST

    KAIST

    KAIST

  • Queen Jeonghui
  • Queen of Joseon from 1455 to 1468

    Yun clan (정경부인 안성군부인 윤씨; 貞敬夫人 安城郡夫人 尹氏; 1417–?) Younger brother − Yun Sa-heun, Duke Yangpyeong, Internal Prince Pacheon (영돈녕 파천부원군 양평공 윤사흔; 領敦寧 坡川府院君 襄平公

    Queen Jeonghui

    Queen_Jeonghui

  • The Host (2006 film)
  • 2006 film by Bong Joon Ho

    the original on November 1, 2024. Retrieved February 17, 2025. Kim, Jae-heun (February 15, 2017). "Korean films influenced US monster movie". The Korea

    The Host (2006 film)

    The_Host_(2006_film)

  • Cation-dependent mannose-6-phosphate receptor
  • Protein found in humans

    PMID 15078902. Kölsch H, Ptok U, Majores M, Schmitz S, Rao ML, Maier W, Heun R (2004). "Putative association of polymorphism in the mannose 6-phosphate

    Cation-dependent mannose-6-phosphate receptor

    Cation-dependent mannose-6-phosphate receptor

    Cation-dependent_mannose-6-phosphate_receptor

  • Female body shape
  • Characteristic of human females

    Young; Chang, Yoosoo; Ahn, Jiin; Yun, Ji-Sup; Park, Yong Lai; Park, Chan Heun; Shin, Hocheol; Ryu, Seungho (30 July 2020). "Menopausal Transition, Body

    Female body shape

    Female body shape

    Female_body_shape

  • SUCLG2
  • Protein-coding gene in the species Homo sapiens

    Holstege H, Kornhuber J, Peters O, Naj AC, Chouraki V, Bellenguez C, Gerrish A, Heun R, Frölich L, Hüll M, Buscemi L, Herms S, Kölsch H, Scheltens P, Breteler

    SUCLG2

    SUCLG2

    SUCLG2

  • Midpoint method
  • Numeric solution for differential equations

    symplectic integrator. Note that the modified Euler method can refer to Heun's method, for further clarity see List of Runge–Kutta methods. The name of

    Midpoint method

    Midpoint method

    Midpoint_method

  • Apolipoprotein AI
  • Protein used in lipid metabolism

    124–129. doi:10.3132/dvdr.2007.030. PMID 17654446. S2CID 23793589. Vollbach H, Heun R, Morris CM, Edwardson JA, McKeith IG, Jessen F, et al. (September 2005)

    Apolipoprotein AI

    Apolipoprotein AI

    Apolipoprotein_AI

  • Prairie School
  • Architectural style

    Elmslie Hugh M. G. Garden Marion Mahony Griffin Walter Burley Griffin Arthur Heun John H. Howe Jens Jensen Henry John Klutho George Washington Maher Mason

    Prairie School

    Prairie School

    Prairie_School

  • Generalized anxiety disorder
  • Nonspecific long-lasting anxiety

    190–211. doi:10.1002/da.20653. PMID 20099273. S2CID 12981577. Barkow K, Heun R, Wittchen HU, Üstün TB, Gänsicke M, Maier W (April 2004). "Mixed anxiety–depression

    Generalized anxiety disorder

    Generalized anxiety disorder

    Generalized_anxiety_disorder

  • AlphaGo
  • Artificial intelligence that plays Go

    Archived from the original on 21 March 2016. Retrieved 18 March 2016. JEE HEUN KAHNG; SE YOUNG LEE (15 March 2016). "Google artificial intelligence program

    AlphaGo

    AlphaGo

  • Lipase A, lysosomal acid type
  • Protein found in humans

    (1): 78–88. doi:10.1086/498851. PMC 1380225. PMID 16385451. von Trotha KT, Heun R, Schmitz S, Lütjohann D, Maier W, Kölsch H (July 2006). "Influence of lysosomal

    Lipase A, lysosomal acid type

    Lipase A, lysosomal acid type

    Lipase_A,_lysosomal_acid_type

  • Heine–Stieltjes polynomials
  • (after Edward Burr Van Vleck) and S is called a Heine–Stieltjes polynomial. Heun polynomials are the special cases of Stieltjes polynomials when the differential

    Heine–Stieltjes polynomials

    Heine–Stieltjes_polynomials

  • Digital differential analyzer
  • and S prior to beginning integration. Other more refined methods such as Heun or Runge-Kutta and implicit Euler can be implemented but are way more hardware

    Digital differential analyzer

    Digital_differential_analyzer

  • Cholesterol 24-hydroxylase
  • Protein family

    Ludwig M, Schulte A, Ptok U, Jessen F, von Bergmann K, Rao ML, Maier W, Heun R (2002). "Polymorphism in the cholesterol 24S-hydroxylase gene is associated

    Cholesterol 24-hydroxylase

    Cholesterol 24-hydroxylase

    Cholesterol_24-hydroxylase

  • Legal status of Germany
  • archives after the Second World War. Translated by Seyer, D. CUP. pp. 219 ff. Heun, Werner (2011). The Constitution of Germany. Hart. Gesetz über das Staatsoberhaupt

    Legal status of Germany

    Legal_status_of_Germany

  • List of numerical analysis topics
  • initial-value problems Midpoint method — a second-order method with two stages Heun's method — either a second-order method with two stages, or a third-order

    List of numerical analysis topics

    List_of_numerical_analysis_topics

  • Mentorship
  • Guidance relationship

    Credibility. San Francisco: Jossey Bass. pp. 155. ISBN 9781555425500. Ensher, E.; Heun, C.; Blanchard, A. (2003). "Online mentoring and computer-mediated communication:

    Mentorship

    Mentorship

    Mentorship

  • One-step method
  • Numerical problem-solving method

    After a group of multi-step methods was presented in 1883, Carl Runge, Karl Heun and Wilhelm Kutta developed significant improvements to Euler's method around

    One-step method

    One-step method

    One-step_method

  • Webtoon (platform)
  • Webtoon hosting service

    Retrieved July 25, 2020. "Doctor Frost". IMDb. Retrieved July 25, 2020. Kim, Jae-heun (May 13, 2015). "Yeo Jin-goo promises romance in "Orange Marmalade"". The

    Webtoon (platform)

    Webtoon (platform)

    Webtoon_(platform)

  • DNA replication
  • Biological process

    nucleus is far smaller than the number of genomic replication forks. P. Heun et al. tracked GFP-tagged replication foci in budding yeast cells and revealed

    DNA replication

    DNA replication

    DNA_replication

  • Neolithic in the Near East
  • world. Oxford: Blackwell Publishers. pp. 144–160. Oliver Dietrich, Manfred Heun, Jens Notroff, Klaus Schmidt and Martin Zarnkow, "The role of cult and feasting

    Neolithic in the Near East

    Neolithic in the Near East

    Neolithic_in_the_Near_East

  • Amelogenesis imperfecta
  • Genetic disorder resulting in abnormal enamel

    PMID 27412008. Seymen, Figen; Kim, Youn Jung; Lee, Ye Ji; Kang, Jenny; Kim, Tak-Heun; Choi, Hwajung; Koruyucu, Mine; Kasimoglu, Yelda; Tuna, Elif Bahar; Gencay

    Amelogenesis imperfecta

    Amelogenesis imperfecta

    Amelogenesis_imperfecta

  • Spherium
  • this becomes a Heun equation with singular points at x = − 1 , 0 , + 1 {\displaystyle x=-1,0,+1} . Based on the known solutions of the Heun equation, we

    Spherium

    Spherium

  • Human artificial chromosome
  • Liskovykh, Mikhail A.; Barrey, Evelyne J.; Larionov, Vladimir; Miga, Karen H.; Heun, Patrick; Black, Ben E. (2019-07-25). "Human Artificial Chromosomes that

    Human artificial chromosome

    Human_artificial_chromosome

  • List of piezoelectric materials
  • ISSN 0002-7820. Park, Hwi-Yeol; Ahn, Cheol-Woo; Song, Hyun-Cheol; Lee, Jong-Heun; Nahm, Sahn; Uchino, Kenji; Lee, Hyeung-Gyu; Lee, Hwack-Joo (2006-08-07)

    List of piezoelectric materials

    List_of_piezoelectric_materials

  • K-pop
  • South Korean popular music genre

    from the original on March 14, 2023. Retrieved March 14, 2023. Kim, Jae-heun (February 18, 2019). "TV guidelines on 'look-alike' K-pop singers spark controversy"

    K-pop

    K-pop

  • Stuttgart
  • Capital of Baden-Württemberg, Germany

    Landeshauptstadt Stuttgart (in German). Retrieved 9 January 2024. Schlaich, Heckel & Heun 1997, p. 28. "Religiöse Vielfalt in einer wachsenden Stadt – Kirche und Religion

    Stuttgart

    Stuttgart

    Stuttgart

  • Dopamine beta-hydroxylase
  • Mammalian protein found in Homo sapiens

    Brown K, Kehoe PG, Barber R, Coto E, Alvarez V, Deloukas P, Gwilliam R, Heun R, Kölsch H, Mateo I, Oulhaj A, Arias-Vásquez A, Schuur M, Aulchenko YS,

    Dopamine beta-hydroxylase

    Dopamine beta-hydroxylase

    Dopamine_beta-hydroxylase

  • List of finite element software packages
  • Euler, implicit Midpoint, Crank-Nicolson, SDIRK. Embedded explicit methods: Heun-Euler, Bogacki-Shampine, Dopri, Fehlberg, Cash-Karp. implicit-euler explicit-euler

    List of finite element software packages

    List_of_finite_element_software_packages

  • List of scientific equations named after people
  • ; Siewert, C. E. (2004). "On computing the Chapman–Enskog and Burnett functions". Journal of Quantitative Spectroscopy and Radiative Transfer. 86 (1):

    List of scientific equations named after people

    List_of_scientific_equations_named_after_people

  • List of linear ordinary differential equations
  • equations List of named differential equations Vallée, Olivier (2004). Airy functions and applications to physics. Internet Archive. Hackensack, NJ : World

    List of linear ordinary differential equations

    List_of_linear_ordinary_differential_equations

  • Megalith
  • Large stone used to build a structure or monument

    Tepe Research Staff. Blog entry 18. Retrieved 2019-08-04. Dietrich, O.; Heun, M.; Notroff, J.; Schmidt, K.; Zarnkow, M. (2012). "The role of cult and

    Megalith

    Megalith

    Megalith

  • Yoo Ah-in
  • South Korean actor (born 1986)

    from the original on October 3, 2015. Retrieved October 6, 2015. Kim, Jae-heun (October 2, 2015). "Yoo Ah-in seeks another success". The Korea Times. Archived

    Yoo Ah-in

    Yoo Ah-in

    Yoo_Ah-in

  • BtoB (band)
  • South Korean boy band

    from the original on March 28, 2019. Retrieved March 24, 2016. Kim, Jae-heun (February 28, 2016). "BTOB sings about spring in 'Remember That'". The Korea

    BtoB (band)

    BtoB (band)

    BtoB_(band)

  • EMV
  • Smart payment card standard

    "Amex joins Visa in postponing US gas EMV migration". 5 May 2020. David Heun (10 September 2012). "MasterCard Brings EMV Chip-Card Liability Policy to

    EMV

    EMV

    EMV

  • Caldwell, New Jersey
  • Borough in Essex County, New Jersey, US

    is governed by a directly elected county executive, with legislative functions performed by the Board of County Commissioners. As of 2025[update], the

    Caldwell, New Jersey

    Caldwell, New Jersey

    Caldwell,_New_Jersey

  • Minjung art
  • South Korean art of the Minjung movement

    (born 1955) Choi Byung Soo (born 1960) Shin Hak-chul Joo Jae-hwan Kim Jeong-heun Min Jeong-ki Kim Yong-tae Minjung Gwangju Uprising (Park, Ki-woong. “Korean

    Minjung art

    Minjung_art

  • Regina Coeli Monastery
  • United States historic place

    was led by Mother Agnes Dwight, Sister Michael Skelley, Sister Magdalen Heun, Sister Raphael Baker, Sister Marie Schuman, and Sister Clare Lafferty. Social

    Regina Coeli Monastery

    Regina Coeli Monastery

    Regina_Coeli_Monastery

  • Rebound effect (conservation)
  • Increase in consumption following energy or resource savings

    Energy Research Centre. Brockway, Paul E.; Sorrell, Steve; Semieniuk, Gregor; Heun, Matthew Kuperus; Court, Victor (May 2021). "Energy efficiency and economy-wide

    Rebound effect (conservation)

    Rebound_effect_(conservation)

  • Gipps' model
  • the previous timestep to generate a more accurate result. For instance, Heun's Method (second order) averages the velocity from the current and previous

    Gipps' model

    Gipps'_model

  • Leimkuhler–Matthews method
  • reduced error compared to the Euler scheme (see e.g. Milstein, Runge-Kutta or Heun's method) these almost always come at an efficiency cost, requiring more computation

    Leimkuhler–Matthews method

    Leimkuhler–Matthews_method

  • Aerobot
  • Flying robot for planetary exploration

    (abstract at smithsonian database, retrieved 13 May 2015) Jack A. Jones and Matt Heun [Montgolfiere Balloon Aerobots for Jupiter’s Atmosphere (Abstract)] Jet Propulsion

    Aerobot

    Aerobot

    Aerobot

  • Heritage preservation in South Korea
  • Platform. Archived from the original on 2014-05-31. Retrieved 2013-07-21. Suh Heun-gang, Ahn Hong-beom. "Fifty Years of Endeavors for Preservation and Transmission"

    Heritage preservation in South Korea

    Heritage preservation in South Korea

    Heritage_preservation_in_South_Korea

  • Felix Arscott
  • British mathematician

    Differential Equations 1987, University of Dundee Numerical Analysis Reports Heun's Differential Equations, Oxford University Press, 1995. (contributor) "Chronicle"

    Felix Arscott

    Felix_Arscott

  • Nucleoplasmin
  • InterPro Family

    www.ebi.ac.uk. Retrieved 2025-12-01. Anselm E, Thomae AW, Jeyaprakash AA, Heun P (November 2018). "Oligomerization of Drosophila Nucleoplasmin-Like Protein

    Nucleoplasmin

    Nucleoplasmin

    Nucleoplasmin

  • Sustainable energy
  • Energy that responsibly meets social, economic, and environmental needs

    Organization 2021, p. 11. Brockway, Paul E.; Sorrell, Steve; Semieniuk, Gregor; Heun, Matthew Kuperus; Court, Victor (May 2021). "Energy efficiency and economy-wide

    Sustainable energy

    Sustainable energy

    Sustainable_energy

  • Wolfgang Grodd
  • German radiologist

    Brain. 126 (Pt 10): 2121–2138. doi:10.1093/brain/awg226. PMID 12902310. Heun, R.; Klose, U.; Jessen, F.; et al. (1999). "Functional MRI of cerebral activation

    Wolfgang Grodd

    Wolfgang Grodd

    Wolfgang_Grodd

  • Scientist of the Month
  • South Korean science award

    synthetic method for Daumone, a longevity-inducing nematode September Lee Heun (이흔) KAIST Biochemical engineering Elucidation of hydrogen storage phenomena

    Scientist of the Month

    Scientist_of_the_Month

  • Stephanie Pace Marshall
  • American educator

    roles, functions, and behavior of women on boards of education in DuPage County, Illinois (Thesis). Loyola University Chicago. OCLC 10014966. Heun, Dave

    Stephanie Pace Marshall

    Stephanie_Pace_Marshall

  • Energy applications of nanotechnology
  • S2CID 93787426. Rai, Prabhakar; Majhi, Sanjit Manohar; Yu, Yeon-Tae; Lee, Jong-Heun (2015). "Noble metal@metal oxide semiconductor core@shell nano-architectures

    Energy applications of nanotechnology

    Energy_applications_of_nanotechnology

  • Günter Breithardt
  • German physician, cardiologist and university professor

    Jürgen Flöge, Jan Galle, Helmut Geiger, Bernd Grabensee, Fokko de Haan, Klaus Heun, Katrin Ivens, Werner Kleophas, Arno Krian, Johannes Kroll, Bernd Kutkuhn

    Günter Breithardt

    Günter Breithardt

    Günter_Breithardt

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HEUN FUNCTION

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HEUN FUNCTION

  • Hun
  • n.

    One of a warlike nomadic people of Northern Asia who, in the 5th century, under Atilla, invaded and conquered a great part of Europe.

  • Hern
  • n.

    A heron; esp., the common European heron.

  • Panel
  • n.

    One of the faces of a hewn stone.

  • Hewn
  • a.

    Roughly dressed as with a hammer; as, hewn stone.

  • Miller
  • n.

    The hen harrier.

  • Peahen
  • n.

    The hen or female peafowl.

  • Hewn
  • a.

    Felled, cut, or shaped as with an ax; roughly squared; as, a house built of hewn logs.

  • Roughhewn
  • a.

    Hewn coarsely without smoothing; unfinished; not polished.

  • Ashler
  • n.

    Hewn or squared stone; also, masonry made of squared or hewn stone.

  • Dandy-cock
  • n. fem.

    Alt. of Dandy-hen

  • Clock
  • v. t. & i.

    To call, as a hen. See Cluck.

  • Eagless
  • n.

    A female or hen eagle.

  • Heuk
  • n.

    Variant of Huke.

  • Hen
  • n.

    The female of the domestic fowl; also, the female of grouse, pheasants, or any kind of birds; as, the heath hen; the gray hen.

  • Wynkernel
  • n.

    The European moor hen.