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Transcendental single-variable function
In mathematics, the Clausen function, introduced by Thomas Clausen (1832), is a transcendental, special function of a single variable. It can be expressed
Clausen_function
Extension of superfactorials to the complex numbers
log-tangent integral on the right-hand side can be evaluated in terms of the Clausen function (of order 2) when 0 < z < 1 {\displaystyle 0<z<1} , as is shown below:
Barnes_G-function
Danish mathematician and astronomer (1801–1885)
discovered the Clausen function. In 1842, Clausen was hired by the staff of the Tartu Observatory, becoming its director in 1866–1872. Works by Clausen include
Thomas Clausen (mathematician)
Thomas_Clausen_(mathematician)
Analytic function in mathematics
{z^{k}}{k^{s}}}} which coincides with the Riemann zeta function when z = 1. The Clausen function Cls(θ) can be chosen as the real or imaginary part of
Riemann_zeta_function
Clausen function Complete Fermi–Dirac integral, an alternate form of the polylogarithm. Dilogarithm Incomplete Fermi–Dirac integral Kummer's function
List of mathematical functions
List_of_mathematical_functions
Mathematical function
A similar result holds for the trigamma function but the circular functions are replaced by Clausen's function. Namely, ψ 1 ( p q ) = π 2 2 sin 2 ( π
Trigamma_function
Number, approximately 0.916
then expressing those Clausen functions in terms of the Barnes G-function, the following expression is obtained (see Clausen function for more):[citation
Catalan's_constant
Cyrillic letter
has since been replaced by ԓ. El is sometimes used to represent the Clausen function, and if not, the capital greek letter Lambda is. Λ λ : Greek letter
El_(Cyrillic)
Topics referred to by the same term
Lobachevsky Prize, including the Lobachevsky Medal Lobachevsky function, also called the Clausen function "Lobachevsky" (song), a humorous song by Tom Lehrer Hyperbolic
Lobachevsky_(disambiguation)
Special case of the polylogarithm
} The function D(z) is sometimes called the Bloch-Wigner function. Lobachevsky's function and Clausen's function are closely related functions. William
Dilogarithm
the OEIS) where Cl 2 {\displaystyle \operatorname {Cl} _{2}} is the Clausen function. This is similar to Catalan's constant G {\displaystyle G} , which
Gieseking_manifold
Special mathematical function
{\displaystyle \psi ^{(n)}(\alpha )=(-1)^{n+1}n!\Phi (1,n+1,\alpha )} The Clausen function: Cl 2 ( z ) = i e − i z 2 Φ ( e − i z , 2 , 1 ) − i e i z 2 Φ ( e i
Lerch_transcendent
Mathematical functions
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied
Lemniscate_elliptic_functions
Numbers expressible as integrals of algebraic functions
a complex number that can be expressed as an integral of an algebraic function over an algebraic domain. The periods are a class of numbers which includes
Period_(number_theory)
Topics referred to by the same term
Wiktionary, the free dictionary. CL2 may refer to: Chlorine gas, Cl2 the Clausen function of order 2, Cl2 the Clifford algebra on C 2 {\displaystyle \mathbb
CL2
Tim Clausen (born 12 March 1969) is a structural biologist and a senior scientist at the Research Institute of Molecular Pathology (IMP) in Vienna, Austria
Tim_Clausen
Mathematical formula by Thomas Clausen
Special functions, Encyclopedia of Mathematics and its Applications, vol. 71, Cambridge University Press, ISBN 978-0-521-62321-6, MR 1688958 Clausen, Thomas
Clausen's_formula
Special mathematical function
polylogarithm with pure imaginary μ may be expressed in terms of the Clausen functions Cis(θ) and Sis(θ), and vice versa (Lewin 1958, Ch. VII § 1.4; Abramowitz
Polylogarithm
This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks
List_of_periodic_functions
Shape in hyperbolic geometry
an ideal tetrahedron can be expressed in terms of the Clausen function or Lobachevsky function of its dihedral angles, and the volume of an arbitrary
Ideal_polyhedron
Arithmetic operation
complex numbers leads to the following paradox, discovered in 1827 by Clausen: For any integer n, we have: e 1 + 2 π i n = e 1 e 2 π i n = e ⋅ 1 = e
Exponentiation
Dyggve-Melchior-Clausen (DMC) Syndrome is a rare autosomal recessive disorder that stunts skeletal and intellectual development. Individuals with this
Dyggve–Melchior–Clausen Syndrome
Dyggve–Melchior–Clausen_Syndrome
Family of power series in mathematics
{\displaystyle n} is a rational function of n {\displaystyle n} . The series, if convergent, defines a generalized hypergeometric function, which may then be defined
Generalized hypergeometric function
Generalized_hypergeometric_function
Large biological molecule that acts as a catalyst
(4): 340–341. doi:10.1634/theoncologist.4-4-340. PMID 10476546. Wu P, Clausen MH, Nielsen TE (December 2015). "Allosteric small-molecule kinase inhibitors"
Enzyme
Rational number sequence
{6}}.\end{cases}}} The von Staudt–Clausen theorem was given by Karl Georg Christian von Staudt and Thomas Clausen independently in 1840. The theorem
Bernoulli_number
Result in number theory showing congruences involving Bernoulli numbers
continuous, so can be extended by continuity to all p-adic integers. Von Staudt–Clausen theorem, another congruence involving Bernoulli numbers Bernoulli number
Kummer's_congruence
Series related to Ramanujan's pi formulas
Oxford: 350–372. Chan; Tanigawa; Yang; Zudilin (2011). "New analogues of Clausen's identities arising from the theory of modular forms". Advances in Mathematics
Ramanujan–Sato_series
Communications protocol
ETags to Reduce Bandwidth & Workload with Spring & Hibernate ETag in HTTP/1.1 specification Concerning Etags and Datestamps by Lars R. Clausen (2004)
HTTP_ETag
minister's son. The police eventually conclude that Aaron's friend Rowan Clausen committed both murders, having always been the instigator for friend activities
List_of_The_Rookie_episodes
7th episode of the 3rd season of The Simpsons
Individual Achievement in Sound Mixing for a Comedy Series or a Special and Alf Clausen for Outstanding Music Composition for a Series. After eating too much Halloween
Treehouse_of_Horror_II
GHB receptor coding gene in the species Homo sapiens
IS, Karim N, Bay T, Olsen JV, Knudsen GM, Bräuner-Osborne H, Frølund B, Clausen RP, Chebib M, Wellendorph P (August 2012). "α4βδ GABA(A) receptors are
GHB_receptor
squares Riemann zeta function Basel problem on ζ(2) Hurwitz zeta function Bernoulli number Agoh–Giuga conjecture Von Staudt–Clausen theorem Dirichlet series
List_of_number_theory_topics
Protein-coding gene in the species Homo sapiens
associated with two types of recessive osteochondrodysplasias, Dyggve-Melchior-Clausen (DMC) syndrome, which involves both skeletal defects and postnatal microcephaly
DYM
Inability to breathe due to body position or posture
ISSN 1088-6222. PMID 21186707. Chan, T. C.; Vilke, G. M.; Neuman, T.; Clausen, J. L. (November 1997). "Restraint position and positional asphyxia". Annals
Positional_asphyxia
Ion channel enzyme pump found in the membrane of all animal cells
2020.588664. PMC 7947867. PMID 33716756. Clausen MV, Hilbers F, Poulsen H (June 2017). "The Structure and Function of the Na,K-ATPase Isoforms in Health
Sodium–potassium_pump
Axioms for the natural numbers
Giuseppe (1908). Formulario Mathematico (V ed.). Turin, Bocca frères, Ch. Clausen. p. 27. Peirce, C. S. (1881). "On the Logic of Number". American Journal
Peano_axioms
Species of bear
December 2021. Retrieved 3 November 2017. Oldfield, C. C.; McHenry, C. R.; Clausen, P. D.; Chamoli, U.; Parr, W. C. H.; Stynder, D. D.; Wroe, S. (2012). "Finite
Giant_panda
Sum of the reciprocal of the Mersenne numbers
157; Knuth attributes the transformation to this form to an 1828 work of Clausen. Erdős, P. (1948), "On arithmetical properties of Lambert series" (PDF)
Erdős–Borwein_constant
Nico Sommer [de] Peter Trabner [de], Annette Frier, Emma Bading, Elvis Clausen [de], Kai Wiesinger Comedy Luna Khaled Kaissar Lisa Vicari, Carlo Ljubek
List of German films of the 2010s
List_of_German_films_of_the_2010s
Removal of the human foreskin
the original on 21 July 2015. Retrieved 3 August 2015. Shabanzadeh DM, Clausen S, Maigaard K, Fode M (2021). "Male Circumcision Complications – A Systematic
Circumcision
maintenance of fluid and electrolyte balance. Potassium is necessary for the function of all living cells and is thus present in all plant and animal tissues
Potassium_in_biology
Military unit
described by one of its leaders as "Schalburg Corps' Group II". Many of Frits Clausen's former supporters in the National Socialist Workers' Party of Denmark
Danish_People's_Defence
Ability to carry out a task
Retrieved on 2009-08-18 Dictionary.com definition. Retrieved on 2009-08-18 Clausen, John A. (ed.) (1968) Socialisation and Society, Boston: Little Brown and
Skill
Function that interpolates text
Format is a function in Common Lisp that can produce formatted text using a format string similar to that of printf. It provides more functionality than
Format_(Common_Lisp)
Infinitely connected triply periodic minimal surface
1802566. doi:10.1002/aenm.201802566. S2CID 106140475. Li, Li; Schulte, Lars; Clausen, Lydia D.; Hansen, Kristian M.; Jonsson, Gunnar E.; Ndoni, Sokol (2011-09-14)
Gyroid
; Andersen, K. K.; Svensson, A. M.; Steffensen, J. P.; Vinther, B. M.; Clausen, H. B.; Siggaard-Andersen, M.-L.; Johnsen, S. J.; Larsen, L. B.; Dahl-Jensen
Timeline of historic inventions
Timeline_of_historic_inventions
Group making loans to developing countries
succeeded by U.S. President Jimmy Carter's nominee, Alden W. Clausen, in 1980. Clausen replaced many members of McNamara's staff and crafted a different
World_Bank_Group
Species of lizard
Matthias J. P.; Moreno, Karen; Ingle, Janette; McHenry, Colin; Ferrara, Toni; Clausen, Phillip; Scheib, Holger; Winter, Kelly L.; Greisman, Laura; Roelants,
Varanus_salvadorii
Volume of air in the lungs at the end of passive expiration
Standardisation of the measurement of lung volumes J. Wanger, J. L. Clausen, A. Coates, O. F. Pedersen, V. Brusasco, F. Burgos, R. Casaburi, R. Crapo
Functional_residual_capacity
German actress (1938–2017)
(1954) The Silent Angel (1954) as Erika Ihre große Prüfung (1955) as Elena Clausen As Long as You Live (1955) as Pepita Santa Lucia (1956) as Manina Kleiner
Karin_Dor
Extinct genus of saber-toothed cat
ISSN 1932-8486. PMC 12506856. PMID 38613218. McHenry, C. R.; Wroe, S.; Clausen, P. D.; Moreno, K.; Cunningham, E. (2007). "Supermodeled sabercat, predatory
Smilodon
Optimization by removing non-optimal solutions to subproblems
problems by breaking them down into smaller subproblems and using a bounding function to eliminate subproblems that cannot contain the optimal solution. It is
Branch_and_bound
Geographical region in Northeast Asia
Crossley 1999 Archived 16 November 2022 at the Wayback Machine, p. 55. Søren Clausen and Stig Thøgersen. The Making of a Chinese City: History and Historiography
Manchuria
Outermost of the three layers that make up the skin
ISBN 978-0-87893-243-6. Weschler CJ, Langer S, Fischer A, Bekö G, Toftum J, Clausen G (May 2011). "Squalene and cholesterol in dust from danish homes and daycare
Epidermis
Earliest major book printed in Europe
at auction". The Guardian. ISSN 0261-3077. Retrieved 13 November 2024. Clausen Books Gutenberg Bible Census Archived 2011-07-08 at the Wayback Machine
Gutenberg_Bible
Chemical compound
G; Saunders, K; White, T; Olsson, ML; Henrissat, B; Sulzenbacher, G; Clausen, H (28 March 2008). "Identification of a GH110 subfamily of alpha 1,3-galactosidases:
Galactose-α-1,3-galactose
American scientist and academic
(born in 1953) is an American researcher who is the A.W. and Mary Margaret Clausen Distinguished Professor Emeritus of Metabolism and Endocrinology at the
Jeffrey_Bluestone
Connection between brain and computer
well-equipped to address the challenges posed by BCI technologies, with Clausen suggesting in 2009 that "BCIs pose ethical challenges, but these are conceptually
Brain–computer_interface
Fictional character from The Simpsons franchise
the way I've heard it." For character songs, Clausen wrote music for lyrics supplied in the scripts. Clausen composed a recurring Sideshow Bob theme for
Sideshow_Bob
State of steady internal conditions maintained by living things
Archived (PDF) from the original on 1 July 2022. Retrieved 30 June 2022. Clausen, M. J.; Poulsen, H. (2013). "Sodium/Potassium Homeostasis in the Cell"
Homeostasis
Canadian actress
Dr. Sophia Jergen Episode: "If Looks Could Kill" 1993 Matrix Marilynn Clausen Episode: "False Witness" 1993 Family Passions Yvonne Haller TV series 1994
Jennifer_Dale
American football player (born 1959)
considered a restrictive culture at BYU, strolled into his first public function with the Bears holding a cold beer in his hand. Head coach Mike Ditka was
Jim_McMahon
Manually operated symmetric encryption cipher
improvements on the basic Nihilist cipher. A very strong version was used by Max Clausen in Richard Sorge's network in Japan, and by Alexander Foote in the Lucy
Nihilist_cipher
Medication
PMID 31643176. Habtemariam BA, Karsten V, Attarwala H, Goel V, Melch M, Clausen VA, et al. (February 2021). "Single-Dose Pharmacokinetics and Pharmacodynamics
Vutrisiran
to operate. Ocean liners are included on this list only if they also functioned as cruise ships. (See: list of ocean liners.) As some cruise ships have
List_of_cruise_ships
Cell organelle that processes proteins
Čaval, Tomislav; Zhu, Jing; Tian, Weihua; Remmelzwaal, Sanne; Yang, Zhang; Clausen, Henrik; Heck, Albert J. R. (2019-01-01). "Targeted Analysis of Lysosomal
Endoplasmic_reticulum
Species of large lamniform shark
2023, p. 44. Wroe, S.; Huber, D. R.; Lowry, M.; McHenry, C.; Moreno, K.; Clausen, P.; Ferrara, T. L.; Cunningham, E.; Dean, M. N.; Summers, A. P. (2008)
Great_white_shark
Molecule that carries genetic information
Biopolymers. 99 (12): 955–68. doi:10.1002/bip.22334. PMC 3844552. PMID 23818176. Clausen-Schaumann H, Rief M, Tolksdorf C, Gaub HE (April 2000). "Mechanical stability
DNA
Roman emperor from 527 to 565
S2CID 189287084. Larsen, L. B.; Vinther, B. M.; Briffa, K. R.; Melvin, T. M.; Clausen, H. B.; Jones, P. D.; Siggaard-Andersen, M.-L.; Hammer, C. U.; et al. (2008)
Justinian_I
Theorem
1007/978-0-8176-4767-4. ISBN 978-0-8176-4766-7. Lee 2012, p. Chapter 18 Clausen 2021, p. Lectures 1 and 3 Lurie, Jacob (2017). Higher Algebra (PDF). pp
De_Rham_theorem
Subgenus of reptiles
W.; Van Osch, M. J.; Moreno, K.; Ingle, J.; McHenry, C.; Ferrara, T.; Clausen, P.; Scheib, H.; Winter, K. L.; Greisman, L.; Roelants, K.; Van Der Weerd
Varanus_(Varanus)
Negationist myth of the American Civil War
cause': the women's group fighting for Confederate monuments". The Guardian. Clausen, Christopher (2000). "Lord Acton and the Lost Cause". The American Scholar
Lost_Cause_of_the_Confederacy
Large animals
150..473K. doi:10.1016/j.agrformet.2009.11.019. Pedrono M, Griffiths OL, Clausen A, Smith LL, Griffiths CJ, Wilmé L, Burney DA (2013-03-01). "Using a surviving
Megafauna
Intelligence test
Man's Guide to Pro Football. Pompei, Dan (April 19, 2010). "Notre Dame's Clausen wild card in NFL draft". Chicago Tribune. Archived from the original on
Wonderlic_test
Topological group structure arising in Fourier analysis
A . {\displaystyle LCA^{op}{\stackrel {\cong }{\longrightarrow }}LCA.} Clausen (2017) shows that the category LCA of locally compact abelian groups measures
Locally_compact_abelian_group
State that has lost its ability to govern
has lost its ability to fulfill fundamental security and development functions, lacking effective control over its territory and borders. Common characteristics
Failed_state
Chancellor of West Germany from 1949 to 1963
October 1950 under which the Federal Republic would have its military forces function as part of the armed wing of the multinational European Defense Community
Konrad_Adenauer
United States historic place
father's firm under the name of Clausen, Kruse and Klein. Both the East and Northwest Turners continued to function in Davenport until at least the 1980s
Northwest Davenport Turner Society Hall
Northwest_Davenport_Turner_Society_Hall
Book by John Stuart Mill
and Utilitarianism: Stanford.{{cite web}}: CS1 maint: location (link) Clausen, Christopher (2009). "John Stuart Mill's 'Very Simple Principle'". Wilson
On_Liberty
Peptide hormone
E553–58. doi:10.1152/ajpendo.90261.2008. PMID 18430962. S2CID 10153197. Clausen T (September 2008). "Regulatory role of translocation of Na+-K+ pumps in
Insulin
1159/000063555. PMID 12207094. S2CID 46833231. Clausen, M.V.; Hilbers, F.; Poulsen, H. (2017). "The Structure and Function of the Na,K-ATPase Isoforms in Health
Sodium_in_biology
English title) Running time: Length of the film as released Type: Genre and function Producer: The producer(s) of the film Director: The director(s) of the
List_of_Nazi_propaganda_films
Family of large reptilian carnivores
April 2013. Wroe, S.; Huber, D. R.; Lowry, M.; McHenry, C.; Moreno, K.; Clausen, P.; Ferrara, T. L.; Cunningham, E.; Dean, M. N.; Summers, A. P. (2008)
Crocodile
Enzyme
Bibcode:1982Sci...215..168G. doi:10.1126/science.6274021. PMID 6274021. Olsson ML, Clausen H (January 2008). "Modifying the red cell surface: towards an ABO-universal
GLA_(gene)
Phylum of microscopic animals
macrodasyidans, Y-shaped cells, each containing a vacuole, surround the gut and may function as a hydrostatic skeleton. The mouth is at the anterior end and opens into
Gastrotrich
Island in the Mediterranean and region of Italy
Science and the Environment – via eoearth.org. Padel Maxime; Sébastien Clausen; José-Javier Alvaro; Josep Maria Casas (2018). "Review of the Ediacaran-Lower
Sardinia
Major volcanic eruption around 1600 BC
2020.41. hdl:10023/20465. ISSN 0033-8222. S2CID 216215614. Hammer, C. U.; Clausen, H. B.; Friedrich, W. L.; Tauber, H. (1987). "The Minoan eruption of Santorini
Minoan_eruption
French businessman (born 1963)
Federation for a two-year term, effective 1 January 2015, succeeding Christian Clausen, president and CEO of Nordea Bank. During his first years in office, Oudéa
Frédéric_Oudéa
Japanese political party
KBS World JAPANESE (in Korean). 12 June 2003. Retrieved 21 March 2023. Clausen, Daniel (24 October 2013). "Japan's persistent pacifism (in English)".
Japanese_Communist_Party
Municipality in Rhineland-Palatinate, Germany
the then classified stocks of GB and VX nerve gas located at Site 59 in Clausen. The nerve agents at Site 59, were removed under Operation Steel Box in
Münchweiler_an_der_Rodalb
Extinct species of deer
Klinkhamer, Ada J.; Woodley, Nicholas; Neenan, James M.; Parr, William C. H.; Clausen, Philip; Sánchez-Villagra, Marcelo R.; Sansalone, Gabriele; Lister, Adrian
Irish_elk
Artificial device that replaces a missing body part
Hansson, Sven Ove (2015), "Ethical Implications of Sensory Prostheses", in Clausen, Jens; Levy, Neil (eds.), Handbook of Neuroethics, Dordrecht: Springer
Prosthesis
Excess production of aldosterone in the adrenal gland
PMID 23416519. S2CID 205346722. Azizan EA, Poulsen H, Tuluc P, Zhou J, Clausen MV, Lieb A, et al. (September 2013). "Somatic mutations in ATP1A1 and CACNA1D
Primary_aldosteronism
Family of ethnic groups of Eurasia
d'Amérique et d'Orient. Reprint: Taipei. Cheng Wen Publishing Co. 1969. Clausen, Gerard. 1972. An etymological dictionary of pre-thirteenth-century Turkish
Turkic_peoples
Marine phylum of animals often with radial symmetries
1093/genetics/iyae002. PMC 11075573. PMID 38262680. Topper, Timothy P.; Guo, Junfeng; Clausen, Sébastien; Skovsted, Christian B.; Zhang, Zhifei (25 March 2019). "A stem
Echinoderm
Outer layer of the cerebrum of the mammalian brain
University Press. p. 533. ISBN 978-0-19-967814-3. Warren N, Caric D, Pratt T, Clausen JA, Asavaritikrai P, Mason JO, et al. (September 1999). "The transcription
Cerebral_cortex
Bulgarian politician and economist
especially the need to provide shelter and health services and to restore the functions and services of the government, so as to start work on reconstruction
Kristalina_Georgieva
https://doi.org/10.1073/pnas.251548698 Oldfield, C. C.; McHenry, C. R.; Clausen, P. D.; Chamoli, U.; Parr, W. C. H.; Stynder, D. D.; Wroe, S. (2012). "Finite
Largest_prehistoric_animals
Period of major evolutionary diversification of animal life
1073/pnas.1110633108. PMC 3158185. PMID 21810989. Chang, Shan; Zhang, Lei; Clausen, Sébastien; Bottjer, David J.; Feng, Qinglai (1 October 2019). "The Ediacaran-Cambrian
Cambrian_explosion
Conspiracy theory about the Pearl Harbor attack
Henry L. Stimson, authorized by Congress and carried out by Henry Clausen (the Clausen Inquiry; 1946); and the Thurmond-Spence hearing, in April 1995, which
Pearl Harbor advance-knowledge conspiracy theory
Pearl_Harbor_advance-knowledge_conspiracy_theory
travel, tourism, insurance
CLAUSEN FUNCTION
CLAUSEN FUNCTION
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travel, tourism, insurance