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Kapteyn series is a series expansion of analytic functions on a domain in terms of the Bessel function of the first kind. Kapteyn series are named after
Kapteyn_series
Infinite series of Bessel functions
} Orthogonality Generalized Fourier series Hankel transform Kapteyn series Neumann polynomial Schlömilch's series Magnus, Wilhelm; Oberhettinger, Fritz;
Fourier–Bessel_series
Fourier series type expansion
}e^{-nz}J_{0}(nr)} is a solution of Laplace equation for z > 0 {\displaystyle z>0} . Kapteyn series Schlomilch, G. (1857). On Bessel's function. Zeitschrift fur Math, and
Schlömilch's_series
Family of solutions to related differential equations
_{q=0}^{N-1}e^{ix\sin {(2q+1)\pi /N}}e^{-i(2q+1)\pi p/N}} A series expansion using Bessel functions (Kapteyn series) is 1 1 − z = 1 + 2 ∑ n = 1 ∞ J n ( n z ) . {\displaystyle
Bessel_function
Orbital mechanics term
\quad M\in [-\pi ,\pi ].} With respect to e {\displaystyle e} , it is a Kapteyn series. The inverse Kepler equation is the solution of Kepler's equation for
Kepler's_equation
Dutch scholar
Olga Fröbe-Kapteyn (19 October 1881 – 25 April 1962) was a Dutch spiritualist. She lived in Switzerland for most of her life, where she founded, in Ascona
Olga_Fröbe-Kapteyn
Observatory
William Herschel Telescope, the Isaac Newton Telescope, and the Jacobus Kapteyn Telescope, operated by a collaboration between the UK Science and Technology
Isaac Newton Group of Telescopes
Isaac_Newton_Group_of_Telescopes
Scottish actor (1938–2005)
(1974) as New Military Governor (uncredited) The Hiding Place (1975) as Kapteyn Erotic Inferno (1975) as Eric Gold Rogue Male (BBC Film) (1976) as Adolf
Michael_Sheard
Intellectual discussion group dedicated to humanistic and religious studies
food, a no-host dinner." The circle at Moscia was founded by Olga Froebe-Kapteyn in 1933, and these conferences have been held annually on the grounds of
Eranos_Foundation
Hypothetical invisible cosmic material
existence of dark matter using stellar velocities was Dutch astronomer Jacobus Kapteyn in 1922. A publication from 1930 by Swedish astronomer Knut Lundmark points
Dark_matter
Canary island
5 m (8 ft 2 in) Isaac Newton Telescope and the 1 m (3 ft 3 in) Jacobus Kapteyn Telescope. The 2.5 m (8 ft 2 in) Nordic Optical Telescope (NOT). The 1 m
La_Palma
Welsh science fiction author (born 1966)
Annual Collection (2012, ISBN 978-1-250-00354-6), Gardner Dozois, ed. "Sad Kapteyn" – Originally published online by the School of Physics and Astronomy,
Alastair_Reynolds
American esoteric, theosophist and writer (1880–1949)
because of personal conflict between Bailey and Froebe-Kapteyn, at which time Froebe-Kapteyn replaced it with the Eranos group.[citation needed] Roberto
Alice_Bailey
Constellations". The Mythology of the Night Sky. Patrick Moore's Practical Astronomy Series. pp. 19–56. doi:10.1007/978-1-4614-0137-7_3. ISBN 978-1-4614-0136-0. S2CID 115168457
List_of_proper_names_of_stars
Galaxy containing the Solar System
Galaxy (M51). In 1904, while studying the proper motions of stars, Jacobus Kapteyn reported that these were not random, as was believed at the time; stars
Milky_Way
Type of laser
2001. Chang, Zenghu; Rundquist, Andy; Wang, Haiwen; Murnane, Margaret M.; Kapteyn, Henry C. (20 October 1997). "Generation of Coherent Soft X Rays at 2.7
X-ray_laser
Concept in sociology and economy
of Economic Research. Kuhn, Peter; Kooreman, Peter; Soetevent, Adriaan; Kapteyn, Arie (2011-08-01). "The Effects of Lottery Prizes on Winners and Their
Conspicuous_consumption
Single yellow-hued star in the constellation Cetus
revised MK types for the cooler stars". Astrophysical Journal Supplement Series. 71: 245. Bibcode:1989ApJS...71..245K. doi:10.1086/191373. "Tau Cet". SIMBAD
Tau_Ceti
Study of the movement of stars
Hercules stream Hyades Stream IC 2391 supercluster (Argus Association) Kapteyn group MBM 12 association TW Hydrae association Ursa Major Moving Group
Stellar_kinematics
Figure in medieval Scandinavian romance
gaelicized Amhlaide) who was the prototype of the English Havelok. N. Kapteyn, 'Zwei Runeninschriften aus der Terp von Westeremden', Beiträge zur Geschichte
Amleth
American philosopher and theologian (born 1932)
their two daughters—Jane (Jane Plantinga Pauw) and Ann (Ann Plantinga Kapteyn)—became a pastor and translator, respectively. Plantinga is the author
Alvin_Plantinga
Originally these locomotives were equipped with a speedometer of the system Kapteyn, which was driven by one of the axles of the bogie. A sanding system of
NS_1600_(steam_locomotive)
1051/0004-6361/202348033. Anglada-Escude, G.; et al. (2014). "Two planets around Kapteyn's star : a cold and a temperate super-Earth orbiting the nearest halo red-dwarf"
List_of_nearest_stars
Psychological concept
York: Academic Press Kuhn, Peter; Kooreman, Peter; Soetevent, Adriaan; Kapteyn, Arie (2011). "The Effects of Lottery Prizes on Winners and Their Neighbors:
Hedonic_treadmill
Classic taoist text
Chung-Yuan (1956). "Self-Realization and the Inner Process of Peace". In Fröbe-Kapteyn (ed.). Eranos Annales (in German) (Olga ed.). Rhein-Verlag. p. 429. Esposito
The Secret of the Golden Flower
The_Secret_of_the_Golden_Flower
These include Gliese 581 d and g, Gliese 667 Ce and f, Gliese 682 b and c, Kapteyn b, Gliese 229 Ac, HD 85512 b and Gliese 832 c. Several other planets, such
List of potentially habitable exoplanets
List_of_potentially_habitable_exoplanets
Specialized agency of the United Nations
The Politics of World Communication. SAGE. p. 8. ISBN 978-1-4462-3437-2. Kapteyn, Paul J. G.; Lauwaars, R. H.; Kooijmans, P. H. (19 October 1982). International
International Telecommunication Union
International_Telecommunication_Union
Apparent faster-than-light motion of distant astronomical objects
..600L..63B. doi:10.1086/381529. S2CID 121645094. Kapteyn's paper Index of citations to Kapteyn's paper Couderc (1939) Annales d'Astrophysique 2, 271
Superluminal_motion
Globular cluster in the constellation Centaurus
dwarf galaxy that was disrupted and absorbed by the Milky Way. Indeed, Kapteyn's Star, which is currently only 13 light-years away from Earth, is thought
Omega_Centauri
Prep school in Deerfield, Massachusetts, US
for soccer and lacrosse. Headmaster's Field is a baseball field. Jamie Kapteyn Field Jim Smith Field is a turf field used for football and boys' lacrosse
Deerfield_Academy
Jacobsohn Maurice Janet Charles Frewen Jenkin Miloš Kössler [cs] Willem Kapteyn [de] Louis Charles Karpinski Arthur Edwin Kennelly Cassius Jackson Keyser
List of International Congresses of Mathematicians Plenary and Invited Speakers
List_of_International_Congresses_of_Mathematicians_Plenary_and_Invited_Speakers
Constellation in the southern celestial hemisphere
40307 g—is a potential super-Earth in the circumstellar habitable zone. Kapteyn's Star, the nearest star in Pictor to Earth, is a red dwarf located 12.76
Pictor
Public health issue in Ireland
original on 23 February 2024. Retrieved 23 February 2024. Delaney, Liam; Kapteyn, Arie; Smith, James P. (1 March 2013). "Why Do Some Irish Drink So Much
Alcoholism_in_Ireland
Method of dating based on the analysis of patterns of tree rings
appearing in forestry textbooks. In the 1870s, the Dutch astronomer Jacobus Kapteyn (1851–1922) was using crossdating to reconstruct the climates of the Netherlands
Dendrochronology
Matter and radiation in the space between the star systems in a galaxy
ether, yet the character of its selective absorption, as indicated by Kapteyn, is characteristic of a gas, and free gaseous molecules are certainly there
Interstellar_medium
Collegiate summer baseball team in Massachusetts
the Bourne Braves two games to one to win the best of three championship series. The title was the team's sixth in the CCBL's modern era and seventh overall
Harwich_Mariners
Dutch astronomer and Marxist theorist (1873–1960)
galaxy. In this research, he adapted the statistical methods of Jacobus Kapteyn to investigate individual clusters in the galaxy. His most important results
Anton_Pannekoek
System of stars and interstellar matter
galaxy with the Solar System close to the center. Using a refined approach, Kapteyn in 1920 arrived at the picture of a small (diameter about 15 kiloparsecs)
Galaxy
Coordination of related astronomical observations
Fermi-LAT, MAGIC, AGILE, ASAS-SN, HAWC, H.E.S.S., INTEGRAL, Kanata, Kiso, Kapteyn, Liverpool Telescope, Subaru, Swift/NuSTAR, VERITAS, VLA/17B-403 teams)
Multi-messenger_astronomy
Dutch chemist and meteorologist (1817–1890)
in 1887. Among his students was the prominent Dutch astronomer Jacobus Kapteyn. Harold L. Burstyn "Buys Ballot, Christoph Hendrik Diederik" Dictionary
C._H._D._Buys_Ballot
Dutch physicist (1888–1966)
work on opalescence in gases. In 1913, he became assistant to Jacobus Kapteyn in the astronomical laboratory at the University of Groningen. In 1914
Frits_Zernike
Class of galaxy that has spiral structures extending from their cores
close to the Sun are thought to belong to the galactic halo, for example Kapteyn's Star and Groombridge 1830. Due to their irregular movement around the
Spiral_galaxy
Science and engineering award presented by the Franklin Institute
2021 Roberto Car Chemistry 2021 Michele Parrinello Chemistry 2021 Henry Kapteyn Physics 2021 Margaret Murnane Physics 2021 Jeremy Nathans Life Science
Franklin_Institute_Awards
Blazar galaxy and source of astrophysical neutrinos
Fermi-LAT, MAGIC, AGILE, ASAS-SN, HAWC, H.E.S.S., INTEGRAL, Kanata, Kiso, Kapteyn, Liverpool Telescope, Subaru, Swift/NuSTAR, VERITAS, VLA/17B-403 teams)
TXS_0506+056
Rotation and X-ray and Ultraviolet Properties of the Halo Population Kapteyn's Star". The Astrophysical Journal. 821 (2): 81. arXiv:1602.01912. Bibcode:2016ApJ
List of nearest stars by spectral type
List_of_nearest_stars_by_spectral_type
Open cluster in the constellation Taurus
motion and the distance of the Praesepe cluster". Publications of the Kapteyn Astronomical Laboratory Groningen. 41: 1. Bibcode:1927PGro...41....1K.
Hyades_(star_cluster)
Star noted for unusual dimming events
periods Stars named after people Wright gives the examples Barnard's Star, Kapteyn's Star, and Przybylski's Star. Roman, Nancy G. (1987). "Identification of
Tabby's_Star
Brown dwarf in the constellation Hydra
8 mas/yr, the third highest after Barnard's Star (10,300 mas/yr) and Kapteyn's Star (8,600 mas/yr). The mass and age of WISE 0855−0714 are neither known
WISE_0855−0714
Overview of the scientific field of astronomy
Galileo Galilei George Ellery Hale William Herschel Edwin Hubble Jacobus Kapteyn Johannes Kepler Gerard Kuiper Joseph-Louis Lagrange Pierre-Simon Laplace
Outline_of_astronomy
Method of microscopic imaging
field which is growing rapidly. The group of Margaret Murnane and Henry Kapteyn at JILA, CU Boulder demonstrated EUV reflection ptychographic imaging in
Ptychography
Last four German WWII war criminals imprisoned in Breda, the Netherlands
Simons [Wikidata], Max van der Stoel, Hans Teengs Gerritsen, Wim Tensen. Jos Kapteyn, Minus Polak and Gerard Veringa were also involved, but refrained from
Breda_Four
Dim, low mass stars on the main sequence
survey of stars Stellar evolution – Changes to stars over their lifespans Kapteyn's Star – Subdwarf star in the constellation Pictor Yerkes luminosity classification –
Red_dwarf
Physical cosmological theory
of dark matter seemed also proven, confirming its inference by Jacobus Kapteyn, Jan Oort, and Fritz Zwicky in the 1920s and 1930s and demonstrating the
Inhomogeneous_cosmology
Brightest star in the constellation Aquila
selected sample of field stars". Astronomy and Astrophysics Supplement Series. 85 (3): 1015–1019. Bibcode:1990A&AS...85.1015M. Monnier, J. D.; Zhao, M;
Altair
British birth control campaigner and palaeobotanist (1880–1958)
North London Collegiate School, where she was a close friend of Olga Fröbe-Kapteyn. One of her teachers Clotilde von Wyss was very fond of her. Stopes primarily
Marie_Stopes
Romanian historian (1907–1986)
1950, Eliade began attending Eranos conferences, meeting Jung, Olga Fröbe-Kapteyn, Gershom Scholem and Paul Radin. He described Eranos as "one of the most
Mircea_Eliade
German astronomer and mathematician (1571–1630)
chronology related to the Star of Bethlehem.", The Star of Bethlehem, Kapteyn Astronomical Institute Barker, Peter and Bernard R. Goldstein: "Theological
Johannes_Kepler
Dutch astronomer
and Groningen. He obtained his PhD at the latter as a student of Jacobus Kapteyn, defending the dissertation The Coefficient of Differential Galactic Absorption
Jean_Jacques_Raimond_Jr.
Gas giant orbiting Epsilon Indi A
Extrasolar Gas Giants and Brown Dwarfs". The Astrophysical Journal Supplement Series. 263 (1): 15. arXiv:2208.05541. Bibcode:2022ApJS..263...15C. doi:10.3847/1538-4365/ac886a
Epsilon_Indi_Ab
13th-century courtly romance by Wirnt von Grafenberg
Azzadac, v. 8853 (cf. Kapteyn ed. Namenverzeichnis, p. 499). Kuyper's summary explains the Steward's device, according to Kapteyn is a golden roebuck or
Wigalois
List of largest planets by size
ROTATION AND X-RAY AND ULTRAVIOLET PROPERTIES OF THE HALO POPULATION KAPTEYN'S STAR*". The Astrophysical Journal. 821 (2): 81. arXiv:1602.01912. Bibcode:2016ApJ
List_of_largest_exoplanets
Election result affecting losing candidate
dependent on how the choice is made for each individual. Stadt, Huib van de; Kapteyn, Arie; Geer, Sara van de (1985). "The Relativity of Utility: Evidence from
Spoiler_effect
subsequent studies, including candidates around Alpha Centauri B (4.36 ly), Kapteyn's Star (12.8 ly), Van Maanen 2 (14.1 ly), Groombridge 1618 (15.9 ly), AD
List_of_nearest_exoplanets
Small star in constellation of Virgo
Geneva Observatory photometric system", Astronomy & Astrophysics Supplement Series, 26: 275–351, Bibcode:1976A&AS...26..275R Warren, W. H. Jr. (1978), "Photoelectric
Ross_128
Binary star system in the constellation of Andromeda
Velocities for 889 Late-Type Stars", The Astrophysical Journal Supplement Series, 141 (2): 503–522, arXiv:astro-ph/0112477, Bibcode:2002ApJS..141..503N,
Groombridge_34
Star in the constellation Eridanus
Epsilon Eridani. The most recent and closest of these encounters was with Kapteyn's Star, which approached to a distance of about 3 ly (0.92 pc) roughly 12
Epsilon_Eridani
Orbits where planets may have liquid surface water
though its mass remains unknown and its parent star is not a Solar analog. Kapteyn b, discovered in June 2014, was thought to is a possible rocky world of
Habitable_zone
Star in the constellation Canis Minor
by METI and the Sónar music festival in Barcelona, Spain transmitted a series of radio signals towards Luyten's star from a radar antenna at Ramfjordmoen
Luyten's_Star
White dwarf in the constellation Pisces
determination of stellar parallaxes with the 60-inch reflector. Fourth series", Contributions from the Mount Wilson Observatory, 182: 1–35, Bibcode:1920CMWCI
Van_Maanen_2
British occultist and writer (1890–1946)
existence of such entities. Fortune also corresponded with Olga Fröbe-Kapteyn, the Dutch esotericist who founded Eranos in Switzerland. She also renewed
Dion_Fortune
to have composed around 68.3% of the early universe. In 1922, Jacobus Kapteyn proposed the existence of dark matter, an unseen force that moves stars
History of gravitational theory
History_of_gravitational_theory
Binary star system in the Cygnus constellation
the second highest known. It was later moved further down the list by Kapteyn's Star and Barnard's Star. 61 Cygni has the sixth highest proper motion
61_Cygni
Gas giant orbiting Epsilon Eridani
Remarkable Stars Observed by HARPS". The Astrophysical Journal Supplement Series. 200 (2): 15. arXiv:1202.2570. Bibcode:2012ApJS..200...15A. doi:10.1088/0067-0049/200/2/15
Epsilon_Eridani_b
Star in the constellation Piscis Austrinus
of ~3600 Stars and Brown Dwarfs". The Astrophysical Journal Supplement Series. 271 (2): 55. arXiv:2312.03639. Bibcode:2024ApJS..271...55K. doi:10.3847/1538-4365/ad24e2
Gliese_887
T-1 Greta de Vries (1967–2006) was the assistant to the director of the Kapteyn Astronomical Institute in Groningen. JPL · 10658 10659 Sauerland 3266 T-1
Meanings of minor-planet names: 10001–11000
Meanings_of_minor-planet_names:_10001–11000
Wagner credit for earlier observation of this pattern. Kapteyn's Star catalogued by Jacobus Kapteyn in 1898 was previously catalogued by B. A. Gould in 1873
List of examples of Stigler's law
List_of_examples_of_Stigler's_law
Rotation and X-ray and Ultraviolet Properties of the Halo Population Kapteyn's Star". The Astrophysical Journal. 821 (2): 81. arXiv:1602.01912. Bibcode:2016ApJ
List_of_star_extremes
Rotation and X-Ray and Ultraviolet Properties of the Halo Population Kapteyn's Star". The Astrophysical Journal. 821 (2): 14. arXiv:1602.01912. Bibcode:2016ApJ
List_of_smallest_known_stars
U.S. Navy research laboratory
Ellis, Jennifer L.; Ding, Chengyuan; Libby, Stephen B.; Jimenez, Jose L.; Kapteyn, Henry C.; et al. (18 March 2014). "Observation and Control of Shock Waves
United States Naval Research Laboratory
United_States_Naval_Research_Laboratory
2622 T-3 Groningen is a city in north-east Netherlands. It is home to the Kapteyn Astronomical Institute of the University of Groningen. JPL · 12652 12653
Meanings of minor-planet names: 12001–13000
Meanings_of_minor-planet_names:_12001–13000
Sun-centered astronomical model
unchallenged for the next hundred years, with minor refinements. Jacobus Kapteyn introduced motion, density, and luminosity to Herschel's star counts, which
Heliocentrism
Star of luminosity class VI under the Yerkes spectral classification system
Subclasses of cool subdwarfs are as following: cool subdwarf Examples: Kapteyn's Star (sdM1), GJ 1062 (sdM2.5) extreme subdwarf Example: APMPM J0559-2903
Subdwarf
European space observatory for astrometry (2013–2025)
supernovae. In November 2017, scientists led by Davide Massari of the Kapteyn Astronomical Institute, University of Groningen, Netherlands released a
Gaia_(spacecraft)
Crater on the Moon
the nearby mare. It forms part of the larger structure called the Balmer-Kapteyn Basin. Balmer lies to the east-southeast of the crater Vendelinus. Balmer
Balmer_(crater)
Australian astronomer and astrophysicist
as a Queen Elizabeth Fellow at Mount Stromlo. Apart from a year in the Kapteyn Institute in Groningen in 1976 and some occasional absences overseas, he
Ken_Freeman_(astronomer)
Day of the year
1848 – Matthew Webb, English swimmer and diver (died 1883) 1851 – Jacobus Kapteyn, Dutch astronomer and academic (died 1922) 1852 – Thomas Price, Welsh-Australian
January_19
American college baseball season
defeating UCLA in the CWS Championship Series in consecutive games, 7–1 and 2–1. The Gamecocks won their first seven SEC series of the 2010 season, which continued
2010 South Carolina Gamecocks baseball team
2010_South_Carolina_Gamecocks_baseball_team
Star in the constellation Andromeda
"Infrared colors of low-mass stars". Astrophysical Journal Supplement Series. 82 (1): 351–394. Bibcode:1992ApJS...82..351L. doi:10.1086/191720. Routray
Ross_248
Study of happiness and quality of life
university where this approach was developed. Other researchers included Arie Kapteyn and Aldi Hagenaars. Some scientists claim that happiness can be measured
Happiness_economics
Astronomical observatory in Ohio, US
other evenings and during the day by special appointment. A monthly lecture series detailing various current topics in astronomy is ongoing. Occasional special
Perkins_Observatory
Educational foundation (1945 to 1968)
which was a particular interest of Mary Conover Mellon. The Bollingen Series of books that it sponsored now includes more than 250 related volumes. The
Bollingen_Foundation
Aleksandrovich Bredikhin) 806 Gyldenia (Hugo Gyldén) 818 Kapteynia (Jacobus Kapteyn) 819 Barnardiana (Edward Emerson Barnard) 827 Wolfiana (Max Wolf) 834 Burnhamia
List of minor planets named after people
List_of_minor_planets_named_after_people
Star in the constellation Cetus
Velocities for 889 Late-Type Stars". The Astrophysical Journal Supplement Series. 141 (2): 503–522. arXiv:astro-ph/0112477. Bibcode:2002ApJS..141..503N.
YZ_Ceti
Astrophysics JIVE – Joint Institute for VLBI in Europe JKT – (telescope) Jacobus Kapteyn Telescope JPL – (organization) Jet Propulsion Laboratory, a research center
List_of_astronomy_acronyms
Type of variable star
RR Lyrae type found outside a cluster was U Leporis, discovered by J. Kapteyn in 1890. The prototype star RR Lyrae was discovered prior to 1899 by Williamina
RR_Lyrae_variable
Overview of science and technology in Spain
Monarchs. The "most religious" policy of this monarchy also justified a whole series of decisions with important consequences for production, science and technology
History of science and technology in Spain
History_of_science_and_technology_in_Spain
Italian theoretical astrophysicist and science educator
in the Department of Physics. In 2019, he became a NOVA Fellow at the Kapteyn Astronomical Institute in the Netherlands, followed by a joint Clay Fellowship
Fabio_Pacucci
Star in the constellation Aquarius
stars within 25 parsecs of the sun". The Astrophysical Journal Supplement Series. 53: 643–711. Bibcode:1983ApJS...53..643J. doi:10.1086/190905. Bopp, B.;
Gliese_876
Star in the constellation Microscopium
Cool Stars from the SPOCS Catalog", The Astrophysical Journal Supplement Series, 168 (2): 297–318, arXiv:astro-ph/0607235, Bibcode:2007ApJS..168..297T,
Lacaille_8760
Variable stars of late spectral types
K and M stars that are BY Draconis variables include Barnard's Star, Kapteyn's Star, 61 Cygni, Ross 248, Lacaille 8760, Lalande 21185, Epsilon Eridani
BY_Draconis_variable
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