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Integral transform used in various branches of mathematics
In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially
Abel_transform
Mapping involving integration between function spaces
edition: Mathematically, what is the kernel in path integral? Assuming the Abel transform is not discontinuous at u {\displaystyle u} . Some conditions apply
Integral_transform
of transforms in mathematics. Abel transform Aboodh transform Bateman transform Fourier transform Fourier cosine transform Fourier sine transform Fractional
List_of_transforms
Norwegian mathematician (1802–1829)
Niels Henrik Abel (/ˈɑːbəl/ AH-bəl, Norwegian: [ˌnɪls ˈhɛ̀nːɾɪk ˈɑ̀ːbl̩]; 5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering
Niels_Henrik_Abel
Mathematical operation
even n − m ≥ 0. Fourier transform Integral transform Abel transform Fourier–Bessel series Neumann polynomial Y and H transforms Louis de Branges (1968)
Hankel_transform
theorem Abel polynomials Abel's summation formula Abelian means Abel's test Abel's theorem Abelian theorem Abel–Ruffini theorem Abel transform Abel transformation
List of things named after Niels Henrik Abel
List_of_things_named_after_Niels_Henrik_Abel
Integral transform useful in probability theory, physics, and engineering
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable
Laplace_transform
Mathematical concept
explanation needed] Taking the inverse Fourier transform of the resulting product {r|k|fk} gives the Abel means Arf of f: A r f ( e 2 π i x ) = ∑ k ∈ Z
Poisson_kernel
Theorem in mathematics
projection onto any projection line will be the Abel transform of f(r). The two-dimensional Fourier transform of f(r) will be a circularly symmetric function
Projection-slice_theorem
Theorem to simplify sums of products of sequences
certain types of sums. It is also called Abel's lemma or Abel transformation, named after Niels Henrik Abel who introduced it in 1826. Suppose { f k }
Summation_by_parts
Remote sensing technique
amount of bending can be related to the refractive index by using an Abel transform on the formula relating bending angle to refractivity. In the case of
Radio_occultation
Norwegian international mathematics prize
The Abel Prize (/ˈɑːbəl/ AH-bəl; Norwegian: Abelprisen [ˈɑ̀ːbl̩ˌpriːsn̩]) is awarded annually by the King of Norway to one or more outstanding mathematicians
Abel_Prize
Used in the summation of divergent series
Niels Henrik Abel and Alfred Tauber. The original examples are Abel's theorem showing that if a series converges to some limit then its Abel sum is the
Abelian and Tauberian theorems
Abelian_and_Tauberian_theorems
Representation theory
Beerends, R. J. (1987), "The Fourier transform of Harish-Chandra's c-function and inversion of the Abel transform", Math. Ann., 277: 1–23, doi:10.1007/BF01457275
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
American mathematician
the following theorem relating the partial sums of a sequence to its Abel transform: lim sup t → 1 − | ∑ k = 1 ∞ t k u k − ∑ k = 1 [ q / log t − 1 ] u
Ralph_Palmer_Agnew
Test for series convergence
In mathematics, Abel's test (also known as Abel's criterion) is a method of testing for the convergence of an infinite series. The test is named after
Abel's_test
Ionized part of Earth's upper atmosphere
the GNSS satellite rise or set behind the Earth. Using an Inverse Abel's transform, a radial profile of refractivity at that tangent point on earth can
Ionosphere
2015 film by Steven Spielberg
plane was shot down over the Soviet Union in 1960—in exchange for Rudolf Abel, a convicted Soviet KGB spy held by the United States, whom Donovan represented
Bridge_of_Spies_(film)
Certain vector fields are the sum of an irrotational and a solenoidal vector field
\cdot \mathbf {r} }dV_{k}} The Fourier transform of a scalar field is a scalar field, and the Fourier transform of a vector field is a vector field of
Helmholtz_decomposition
Conditions for switching order of integration in calculus
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Fubini's_theorem
Differential operator in mathematics
^{n}} , the Laplacian is particularly simple after applying the Fourier transform. With the convention f ^ ( ξ ) = ∫ R n f ( x ) e − 2 π i x ⋅ ξ d x , {\displaystyle
Laplace_operator
Multivariate derivative (mathematics)
p} gives the direction and the rate of fastest increase. The gradient transforms like a vector under change of basis of the space of variables of f {\displaystyle
Gradient
1914 opera by Felix Weingartner
Kain und Abel is a one-act opera by Austrian conductor and composer Felix Weingartner, who also wrote the libretto. The work was composed in the early
Kain_und_Abel
Curve for which the time to roll to the end is equal for all starting points
compute its Laplace transform, calculate the Laplace transform of d ℓ / d y {\displaystyle {d\ell }/{dy}} and then take the inverse transform (or try to) to
Tautochrone_curve
Infinite sum
by Abel, but the first to attack it successfully were Seidel and Stokes (1847–48). Cauchy took up the problem again (1853), acknowledging Abel's criticism
Series_(mathematics)
Mathematical identities
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Vector_calculus_identities
Technique in integral evaluation
Leibniz's notation for integrals and derivatives. The formula is used to transform one integral into another integral that is easier to compute. Thus, the
Integration_by_substitution
Integral of sin(x)/x from 0 to infinity
{1}{s^{2}+1}}} , which is the Laplace transform of the function sin t {\displaystyle \sin t} as well as a version of Abel's theorem (a consequence of the final
Dirichlet_integral
Branch of mathematical analysis
order 1/2. Fractional calculus was introduced in one of Niels Henrik Abel's early papers where all the elements can be found: the idea of fractional-order
Fractional_calculus
Matrix of second derivatives
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Hessian_matrix
Mathematical method in calculus
product of their derivative and antiderivative. It is frequently used to transform the antiderivative of a product of functions into an antiderivative for
Integration_by_parts
Matrix of partial derivatives of a vector-valued function
"rotating" or "transforming" that the function imposes locally near that point. For example, if (x′, y′) = f(x, y) is used to smoothly transform an image,
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Method of evaluating certain integrals along paths in the complex plane
contour are determined by its values along the contour. The inverse Laplace transform is defined by a complex contour integral known as the Bromwich integral:
Contour_integration
Integral transform
possibility of fractional calculus in 1832. The operator agrees with the Euler transform, after Leonhard Euler, when applied to analytic functions. It was generalized
Riemann–Liouville_integral
Theorem in mathematics
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Mean_value_theorem
Relation between pairs of arithmetic functions
the corresponding Dirichlet series: each repeated application of the transform corresponds to multiplication by the Riemann zeta function. A related
Möbius_inversion_formula
Identity relating to differential equations
In mathematics, Abel's identity (also called Abel's formula or Abel's differential equation identity) is an equation that expresses the Wronskian of two
Abel's_identity
Theorem in vector calculus
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Stokes'_theorem
Instantaneous rate of change (mathematics)
S2CID 259885793 Debnath, Lokenath; Shah, Firdous Ahmad (2015), Wavelet Transforms and Their Applications (2nd ed.), Birkhäuser, doi:10.1007/978-0-8176-8418-1
Derivative
Circulation density in a vector field
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Curl_(mathematics)
1995 video game
man named Abel who must rescue his wife and child from hell. It is a 2D side scrolling game. Defeating bosses allows the player to transform into various
Majūō
Infinite series with alternating signs
, so the series is an example where a slightly stronger method, such as Abel summation, is required. The series 1 − 2 + 3 − 4 + ... is closely related
1_−_2_+_3_−_4_+_⋯
Formula in calculus
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Chain_rule
Differentiation under the integral sign formula
of integral transforms. An example of such is the moment generating function in probability theory, a variation of the Laplace transform, which can be
Leibniz_integral_rule
Mathematical operation in calculus
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Implicit_differentiation
Differential calculus on function spaces
quantity. In this case, this quantity is the Hamiltonian, the Legendre transform of the Lagrangian, which (often) coincides with the energy of the system
Calculus_of_variations
Theorem in mathematics
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Inverse_function_theorem
Operation in mathematical calculus
definite integrals; for instance, Parseval's identity can be used to transform an integral over a rectangular region into an infinite sum. Occasionally
Integral
Mathematical criterion about whether a series converges
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Convergence_tests
Method of mathematical integration
This is important, for instance, in the study of Fourier series, Fourier transforms, and other topics. The Lebesgue integral describes better how and when
Lebesgue_integral
Peer-to-peer review site
employees of BigMachines – Tim Handorf, Godard Abel, Matt Gorniak, Mark Myers and Mike Wheeler – founded G2, with Abel serving as president. The company focused
G2_(company)
Experimental velocity measurement technique
recovered from the two-dimensional projection by the use of the inverse Abel transform. The cylindrical axis is the axis containing the polarization direction
Photofragment-ion_imaging
Relation between frequency- and time-domain behavior at large time
t ) {\displaystyle f(t)} in continuous time has (unilateral) Laplace transform F ( s ) {\displaystyle F(s)} , then a final value theorem establishes
Final_value_theorem
German mathematician (1804–1851)
series. The solution of the Jacobi inversion problem for the hyperelliptic Abel map by Weierstrass in 1854 required the introduction of the hyperelliptic
Carl_Gustav_Jacob_Jacobi
On converting relations to functions of several real variables
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Implicit_function_theorem
German-American economist (1910–2007)
Richard Abel Musgrave (14 December 1910 – 15 January 2007) was an American economist of German heritage. His most cited work is The Theory of Public Finance
Richard_Musgrave_(economist)
Formula for the derivative of a ratio of functions
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Quotient_rule
Mathematical approximation of a function
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Taylor_series
Type of derivative in mathematics
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Derivative (multivariable calculus)
Derivative_(multivariable_calculus)
Mathematical operation
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Second_derivative
Summation method for some divergent series
Binomial transform Borel summation Cesàro summation Lambert summation Perron's formula Abelian and Tauberian theorems Abel–Plana formula Abel's summation
Euler_summation
laboratory of a mad scientist named Dr. Abel in his attempt to complete his project of forming a cyborg army. Abel thought that a perfect cyborg must have
Characters of the Tekken series
Characters_of_the_Tekken_series
Derivative of a function with multiple variables
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Partial_derivative
Formula for the derivative of a product
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Product_rule
Vector operator in vector calculus
appears twice, here, once, so that the X a {\displaystyle X^{a}} can be transformed into "flat space" (where coordinates are actually orthonormal), and once
Divergence
Relationship between derivatives and integrals
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Spanish football manager (born 1970)
Enrique became Celta de Vigo's new manager, replacing former national teammate Abel Resino. He led the Galicians to the ninth position in his only season, highlights
Luis_Enrique
Operator in fractional calculus
{\displaystyle f(t)} is equal to zero. Moreover, a form of the Laplace transform allows to simply evaluate the initial conditions by computing finite,
Differintegral
Vector calculus formulas relating the bulk with the boundary of a region
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Green's_identities
(b. 1932) Blanquita Valenti, 87, politician (b. 1933/1934) March 10 Bruce Abel, 84, bass singer (b. 1936) Eugene Hughes, 86, academic administrator, president
2021 deaths in the United States (January–June)
2021_deaths_in_the_United_States_(January–June)
Infinite series that is not convergent
translated as "Divergent series are an invention of the devil …") — N. H. Abel, letter to Holmboe, January 1826, reprinted in volume 2 of his collected
Divergent_series
Study of rates of change
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Differential_calculus
Method for partial-fraction expansion
482-489 Zill, Dennis G.; Wright, Warren S. (2013). "Chapter 7: The Laplace Transform". Differential Equations with Boundary-Value Problems (8th ed.). Brooks/Cole
Heaviside_cover-up_method
Course designed to prepare students for calculus
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Precalculus
of elementary and special functions, volume 4–5 are tables of Laplace transforms). More compact collections can be found in e.g. Brychkov, Marichev, Prudnikov's
Lists_of_integrals
American multinational technology company
the original on January 6, 2022. Retrieved January 6, 2022. Ekene, Mfon Abel (August 6, 2024). "Google says it is obligated to disclose confidential information
Ritsuka and Mash, with him now recognizing Mash's newfound strength. Jingle Abel Meuniere (ジングル・アベル・ムニエル, Jinguru Aberu Munieru) Voiced by: Jizoudou Takehiro
List of Fate/Grand Order characters
List_of_Fate/Grand_Order_characters
Integrals not expressible in closed-form from elementary functions
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Nonelementary_integral
Mathematics award
survey conducted by IREG in 2013–14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics.
Fields_Medal
Mathematical operation in calculus
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Logarithmic_derivative
Mathematical technique for simplification
polynomial equations are generally impossible to solve in terms of radicals (see Abel–Ruffini theorem). This particular equation, however, may be written ( x 3
Change_of_variables
Lucihormetica luckae Semachrysa jade Juracimbrophlebia ginkgofolia 2012 Abel Prize: Endre Szemerédi 2012 Fundamental Physics Prize: Nima Arkani-Hamed
2012_in_science
Statement relating differentiable symmetries to conserved quantities
field themselves and changes in coordinates, since the transformed field αA depends on the transformed coordinates ξμ. To isolate the intrinsic changes, the
Noether's_theorem
Rate of change of the second derivative
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Third_derivative
Island country in the Pacific Ocean
subsequently developed a distinctive Māori culture. In 1642, the Dutch explorer Abel Tasman became the first European to sight and record New Zealand. In 1769
New_Zealand
Ang Lee George Lucas Alan Ball, American writer, director and producer. Abel Ferrara, American filmmaker, known for the provocative and often controversial
List_of_American_Buddhists
Mathematical term; type of polynomial transformation
Ehrenfried Walther von Tschirnhaus in 1683. Simply, it is a method for transforming a polynomial equation of degree n ≥ 2 {\displaystyle n\geq 2} with some
Tschirnhaus_transformation
Indefinite integral
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Antiderivative
Special function in the physical sciences
Fourier transform requires y to decay to zero fast enough; Bi grows to infinity exponentially fast, so it cannot be obtained via a Fourier transform. The
Airy_function
American film soundtrack label
the Tombstones – Carlos Rafael Rivera VSD-7298 Penny Dreadful: Season 1 – Abel Korzeniowski VSD-7299 Chuck – Tim Jones VSD-7303 The Loft – John Frizzell
Varèse Sarabande albums discography
Varèse_Sarabande_albums_discography
Generalization of the product rule in calculus
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
General_Leibniz_rule
Scientific principles enabling the use of the calculus of variations
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Variational_principle
Method for evaluating indefinite integrals
specialist in computer algebra who developed it in 1968. The algorithm transforms the problem of integration into a problem in algebra. It is based on the
Risch_algorithm
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
List_of_calculus_topics
Canadian rapper and singer (born 1986)
from the original on February 26, 2023. Retrieved April 2, 2023. Shifferaw, Abel (June 24, 2023). "Drake Announces New Album With Poetry Book". Complex. Retrieved
Drake_(musician)
Mathematical theorem
action of operators on Schwartz functions on the plane. Under Fourier transform, the difference and differential operators are just multiplication operators
Symmetry of second derivatives
Symmetry_of_second_derivatives
Events of California governorship since 2019
of San Francisco, defeated the Incumbent Republican lieutenant governor Abel Maldonado in the 2010 elections. Newsom started his four-year term as the
Governorship_of_Gavin_Newsom
Howard Wang (English) Abel Walker (アベル・ウォーカー, Aberu Wōkā) is the prefect of Lang House and the leader of the Magia Lupus. Abel is a noble who believes
List_of_Mashle_characters
Performance art by Abel Azcona
pederastia" in Spanish), is a conceptual, critical and process artwork by Abel Azcona. Over several months, Azcona (who had received a Catholic education
Amen_or_The_Pederasty
inconsistently cooked and loaded with raw spices, while Arnold's entree didn't transform her ingredients enough.) 312 9 "Bizarre Battle" Marcus Samuelsson, Marc
List of Chopped episodes (seasons 21–40)
List_of_Chopped_episodes_(seasons_21–40)
ABEL TRANSFORM
ABEL TRANSFORM
Male
African
breath, vapor; transitoriness.
Female
English
Medieval short form of English Amabel, MABEL means "lovable."Â
Male
Hebrew
Variant spelling of Hebrew Abie, ABEY means "father of a multitude."
Biblical
mourning to the house of Maachah,meadow of the house of Maachah,also called ABEL-MAIM
Male
English
Anglicized form of Hebrew Abiy'el, ABIEL means "El (God) is (my) father." In the bible, this is the name of Saul's grandfather.
Boy/Male
Indian
Healthy, Vanity, Breath, Breathing
Boy/Male
Hebrew
Exhalation of breath. The second son of Adam in the bible. The variant Able is used as an English...
Biblical
a city; mourning,vanity; breath; transitoriness
Male
Hungarian
Hungarian form of Greek Habel, �BEL means "vanity," i.e. "transitory."
Male
Italian
Italian form of Hebrew Hebel, ABELE means "breath, breathing."
Surname or Lastname
English
English : variant spelling of Abel. Probably also an Americanized spelling of the same surname in other languages.
Male
English
Breath
Male
English
Variant spelling of English Abel, ABELL means "vanity," i.e. "transitory."
Male
English
 In the bible, this is the name of the second son of Adam and Eve who was killed by his jealous brother Cain. Anglicized form of Greek Habel, ABEL means "vanity," i.e. "transitory." Anglicized form of Hebrew Hebel, meaning "breath, breathing."
Boy/Male
American, Australian, British, Chinese, Christian, Danish, Dutch, English, Finnish, French, German, Hawaiian, Hebrew, Indian, Irish, Norwegian, Polish, Portuguese, Romanian, Swedish
Breath; Highborn and Steadfast; Child; Breathing Spirit; Son; Vapour
Boy/Male
Hebrew
Exhalation of breath. The second son of Adam in the bible. The variant Able is used as an English...
Male
English
Variant spelling of English Abel, ABLE means "vanity," i.e. "transitory."
Boy/Male
Biblical American Hebrew
Vanity, breath, vapor. Also a city, mourning'.
Female
German
German form of Greek Barbara, BÄRBEL means "foreign; strange."
Male
Scandinavian
Scandinavian form of Hebrew Abiyshalowm, AXEL means "father of peace."Â
ABEL TRANSFORM
ABEL TRANSFORM
Male
Hindi/Indian
(पà¥à¤°à¤®à¥‹à¤¦) Hindi name PRAMOD means "happiness, joy."
Boy/Male
Indian
Brave and Cute
Boy/Male
Hindu
Originating in the mind, Born of the mind
Boy/Male
Indian
End of Direction
Girl/Female
Arabic, Muslim
Wisdom; Knowledge; Justice
Boy/Male
Hindu
Master of the Moon
Female
Native American
Native American Navajo name SHADI means "older sister." Compare with masculine forms of Shadi.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
The Holy Trinity
Boy/Male
Gujarati, Hindu, Indian, Malayalam, Marathi, Sindhi, Telugu
One who Stays in Heaven
Girl/Female
Gujarati, Hindu, Indian, Malayalam, Marathi, Sindhi, Telugu
Loved One; The Dearest One
ABEL TRANSFORM
ABEL TRANSFORM
ABEL TRANSFORM
ABEL TRANSFORM
ABEL TRANSFORM
p. pr. & vb. n.
of Abet
n.
A slip of silk, paper, parchment, etc., affixed to anything, usually by an inscription, the contents, ownership, destination, etc.; as, the label of a bottle or a package.
imp. & p. p.
of Abet
a.
Able to sway.
p. pr. & vb. n.
of Label
a.
To make able; to enable; to strengthen.
v. t.
To affix in or on a label.
a.
Able to speak.
superl.
Specially: Having intellectual qualifications, or strong mental powers; showing ability or skill; talented; clever; powerful; as, the ablest man in the senate; an able speech.
v. t.
To affix a label to; to mark with a name, etc.; as, to label a bottle or a package.
adv.
To childbed (in the phrase "brought abed," that is, delivered of a child).
imp. & p. p.
of Label
v. t.
To instigate or encourage by aid or countenance; -- used in a bad sense of persons and acts; as, to abet an ill-doer; to abet one in his wicked courses; to abet vice; to abet an insurrection.
superl.
Legally qualified; possessed of legal competence; as, able to inherit or devise property.
a.
Able to digest.
superl.
Having sufficient power, strength, force, skill, means, or resources of any kind to accomplish the object; possessed of qualifications rendering competent for some end; competent; qualified; capable; as, an able workman, soldier, seaman, a man able to work; a mind able to reason; a person able to be generous; able to endure pain; able to play on a piano.