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Function used to generate other functions
In physics, and more specifically in Hamiltonian mechanics, a generating function is, loosely, a function whose partial derivatives generate the differential
Generating_function_(physics)
Topics referred to by the same term
error) Generating function (math) Generating function (physics) Generating set Generating set of a group Generating trigonometric tables Generating a curve
Generate
Set of quantities in probability theory
the cumulant generating function (CGF) K(t), which is a generating function that is the natural logarithm of the moment generating function: K ( t ) = log
Cumulant
Description of physical properties at the atomic and subatomic scale
Quantum mechanics, also known as quantum physics, is the fundamental physical theory that describes the behavior of matter and of light; the behaviors
Quantum_mechanics
Function that encodes the dependence of a coupling parameter on the energy scale
In theoretical physics, specifically quantum field theory, a beta function or Gell-Mann–Low function, β(g), encodes the dependence of a coupling parameter
Beta_function_(physics)
Summability method in physics
In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent
Zeta_function_regularization
Element of interest in an algebraic structure
In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case
Generator_(mathematics)
Generating function for quantum correlation functions
In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral
Partition function (quantum field theory)
Partition_function_(quantum_field_theory)
Type of energy
In solid-state physics, the work function is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the
Work_function
Description of continuous random distribution
probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given
Probability_density_function
Generating function in integrable systems
Tau functions also appear as matrix model partition functions in the spectral theory of random matrices, and may also serve as generating functions, in
Tau function (integrable systems)
Tau_function_(integrable_systems)
Measure of the shape of a function
moments of a function are certain quantitative measures related to the shape of the function's graph. For example, in physics, if the function represents
Moment_(mathematics)
Scientific field of study
the field of physics is called a physicist. Physics is one of the oldest academic disciplines. Over much of the past two millennia, physics, chemistry,
Physics
Family of solutions to related differential equations
roots of the first few spherical Bessel functions are: The spherical Bessel functions have the generating functions 1 z cos ( z 2 − 2 z t ) = ∑ n = 0 ∞
Bessel_function
Special mathematical function defined as sin(x)/x
In mathematics, physics and engineering, the sinc function (/ˈsɪŋk/), denoted by sinc(x), is defined as either sinc ( x ) = sin x x {\displaystyle
Sinc_function
Ratio of polynomial functions
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator
Rational_function
Study of physics on quintillionth-second timescales
Attosecond physics, also known as attophysics, or more generally attosecond science, is a branch of physics that deals with light–matter interaction phenomena
Attosecond_physics
Description of a quantum-mechanical system
"Schrödinger's original struggles with a complex wave function". American Journal of Physics. 88 (6): 433–438. Bibcode:2020AmJPh..88..433K. doi:10.1119/10
Schrödinger_equation
Generalized coordinates Generalized valence bond Generating function (physics) Generation (particle physics) Generation–recombination noise Generator (mathematics)
Index_of_physics_articles_(G)
Sequence of differential equation solutions
The generating function for them is ∑n=0∞tnLn(α)(x)=1(1−t)α+1e−tx/(1−t). Laguerre functions are defined by confluent hypergeometric functions and Kummer's
Laguerre_polynomials
Response of an optical system to a point source of light
mathematics and physics, these might be referred to as Green's functions or impulse response functions. PSFs are considered impulse response functions for imaging
Point_spread_function
Some of the major unsolved problems in physics are theoretical, meaning that existing theories are currently unable to explain certain observed phenomena
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Physical characteristic of oscillating systems
spin resonance (ESR) and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency (e.g., musical
Resonance
of special functions which developed out of statistics and mathematical physics. A modern, abstract point of view contrasts large function spaces, which
List of mathematical functions
List_of_mathematical_functions
Systematic procedure of turning a classical theory into a quantum one
procedure is basic to theories of atomic physics, chemistry, particle physics, nuclear physics, condensed matter physics, and quantum optics. In 1901, when
Quantization_(physics)
Amount of energy transferred or converted per unit time
Wikimedia Commons has media related to Power (physics). Wikiquote has quotations related to Power (physics). Simple machines Orders of magnitude (power)
Power_(physics)
State of matter
academic field of plasma science or plasma physics, including several sub-disciplines such as space plasma physics. Plasmas can appear in nature in various
Plasma_(physics)
Theoretical framework in physics
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines field theory, special relativity and quantum mechanics. QFT
Quantum_field_theory
Generalized function whose value is zero everywhere except at zero
theory of distributions. The delta function is named after physicist Paul Dirac, and has been applied routinely in physics and engineering to model point
Dirac_delta_function
Wigner distribution function in physics as opposed to in signal processing
probability distribution in phase space. It is a generating function for all spatial autocorrelation functions of a given quantum-mechanical wavefunction ψ(x)
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Millennium Prize Problem
existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined
Yang–Mills existence and mass gap
Yang–Mills_existence_and_mass_gap
Collection of statistical data sets
Justin; Fitzmaurice, George (2017-05-02). "Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated
Datasaurus_dozen
Mathematical function having a characteristic S-shaped curve or sigmoid curve
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the
Sigmoid_function
Multivalued function in mathematics
quantum-mechanical double-well Dirac delta function model for equal charges—a fundamental problem in physics. Prompted by this, Rob Corless and developers
Lambert_W_function
Ordered exponential field Exponential formula Exponential function Exponential generating function Exponential-Golomb coding Exponential growth Exponential
List_of_exponential_topics
Quantum field theory
Unsolved problem in physics Yang–Mills theory and the mass gap. Quantum particles described by the theory have mass but the classical waves of the field
Yang–Mills_theory
Method in which data is created algorithmically as opposed to manually
video games, aiding in generating levels, textures and complete worlds with little human contribution. Procedurally generated elements have appeared in
Procedural_generation
lambda rings. In combinatorics, the plethystic exponential is a generating function for many well studied sequences of integers, polynomials or power
Plethystic_exponential
Physical quantity
the conservation of energy is a consequence of the fact that the laws of physics do not change over time. Thus, since 1918, theorists have understood that
Energy
"Generating massive complex networks with hyperbolic geometry faster in practice". arXiv:1606.09481 [cs.DS]. Penschuck, Manuel (2017). Generating Practical
Hyperbolic_geometric_graph
Special mathematical functions defined on the surface of a sphere
and λ {\displaystyle \lambda } as real parameters. In naming this generating function after Herglotz, we follow Courant & Hilbert 1962, §VII.7, who credit
Spherical_harmonics
Software generating fractal images
Fractal-generating software is any type of graphics software that generates images of fractals. There are many fractal generating programs available,
Fractal-generating_software
Interpretation of quantum mechanics
approximations in physics. MWI originated in Everett's Princeton University PhD thesis "The Theory of the Universal Wave Function", developed under his
Many-worlds_interpretation
Type of differential equation
letter Δ denotes the Laplace operator; if u is a function of n variables, then Δu=u11+u22+⋯+unn. In the physics literature, the Laplace operator is often denoted
Partial_differential_equation
Special functions of several complex variables
theta functions have useful applications in topics such as number theory: "in how many ways can a number be written as a sum of squares?" physics: "how
Theta_function
Analytic function in mathematics
continuation elsewhere. The Riemann zeta function plays a pivotal role in analytic number theory and has applications in physics, probability theory, and applied
Riemann_zeta_function
Mathematical function
Bell-shaped function Cauchy distribution Normal distribution Radial basis function kernel Squires, G. L. (2001-08-30). Practical Physics (4 ed.). Cambridge
Gaussian_function
Intrinsic quantum property of particles
Group Theory in Physics: An Introduction to Symmetry Principles, Group Representations, and Special Functions In Classical And Quantum Physics. London, England
Spin_(physics)
Conjecture in algebraic geometry
these partition functions gives Witten's conjecture that a certain generating function formed from intersection numbers should satisfy the differential
Witten_conjecture
Application of computer graphics to create or contribute to images
where the vision of the simulated camera is not constrained by the laws of physics. Availability of CGI software and increased computer speeds have allowed
Computer-generated_imagery
Relationship between fields of study
the axiomatization of physics as his sixth problem. The problem remains open. In 1930, Paul Dirac invented the Dirac delta function for quantum mechanics
Relationship between mathematics and physics
Relationship_between_mathematics_and_physics
Rate of change of acceleration with time
a jolt in physics?". Physics Network. Retrieved May 11, 2025. "What is the term used for the third derivative of position?". Usenet Physics FAQ. Retrieved
Jerk_(physics)
in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for
Exponential_formula
Retarding force on a body moving in a fluid
immobile pipe restricts the velocity of the fluid through the pipe. In the physics of sports, drag force is necessary to explain the motion of balls, javelins
Drag_(physics)
Class of exact solutions to the Einstein field equations
and by Delgaty & Lake, 2000: Fodor shows how to generate ssspf solutions using one generating function and differentiation and algebraic operations, but
Static spherically symmetric perfect fluid
Static_spherically_symmetric_perfect_fluid
European particle physics research centre
generated 49 petabytes of data. CERN's main function is to provide the particle accelerators and other infrastructure needed for high-energy physics research
CERN
Mathematical function, used to describe magnetization
that considers quantum physics. The Langevin function could then be seen as a special case of the more general Brillouin function if the quantum number
Brillouin and Langevin functions
Brillouin_and_Langevin_functions
Probability distribution
fractional absolute moments exist. The Cauchy distribution has no moment generating function. In mathematics, it is closely related to the Poisson kernel, which
Cauchy_distribution
Type of regression analysis
possible to solve the symbolic regression problem exactly by generating every possible function (built from some predefined set of operators) and evaluating
Symbolic_regression
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
Invariance of operations under geometric translation
In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation (without rotation). Discrete
Translational_symmetry
Physical quantities taking values at each point in space and time
descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another vector field, while electrodynamics
Field_(physics)
This glossary of physics is a list of definitions of terms and concepts relevant to physics, its sub-disciplines, and related fields, including mechanics
Glossary_of_physics
Concept in theoretical computer science
states. A program that generated a longer output must necessarily continue generating forever, i.e. cannot terminate. It is generally undecidable whether a
Busy_beaver
German mathematician (born 1961)
L. (1998). "A conjectural generating function for numbers of curves on surfaces". Communications in Mathematical Physics. 196 (3): 523–533. arXiv:alg-geom/9711012
Lothar_Göttsche
Theoretical problem in quantum physics
Hendrik (2013). "Models of wave-function collapse, underlying theories, and experimental tests". Reviews of Modern Physics. 85 (2): 471–527. arXiv:1204.4325
Measurement_problem
Statement relating differentiable symmetries to conserved quantities
calculus (known by various names in physics such as the Generalized Stokes theorem or the Gradient theorem): for a function S analytical in a domain 𝒟, ∫𝒫dS=0
Noether's_theorem
Idealization of a large number of atomic-sized systems
In physics, specifically statistical mechanics, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies
Ensemble (mathematical physics)
Ensemble_(mathematical_physics)
Function defined by a hypergeometric series
hypergeometric function 2F1(a, b; c; z) is a special function represented by the hypergeometric series, that includes many other special functions as specific
Hypergeometric_function
Mathematical function
M. D. (2017). "Square series generating function transformations" (PDF). Journal of Inequalities and Special Functions. 8 (2). arXiv:1609.02803. Weisstein
Ramanujan_theta_function
Multifractal function used in terrain modeling and simulation
object with applications in physics and mathematics. Berry and Lewis provided computer-generated visualizations of the function, helping establish it as
Weierstrass–Mandelbrot function
Weierstrass–Mandelbrot_function
Theory of the strong nuclear interactions
In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Quarks are fundamental
Quantum_chromodynamics
Special function defined by an integral
&&x\neq 0.\end{aligned}}} The function Ein {\displaystyle \operatorname {Ein} } is related to the exponential generating function of the harmonic numbers:
Exponential_integral
Natural sciences as described by Aristotle
Aristotelian physics is the form of natural philosophy described in the works of the Greek philosopher Aristotle (384–322 BC). In his work Physics, Aristotle
Aristotelian_physics
Number of ways to pair up n objects
Philippe; Gardy, Danièle; Gouyou-Beauchamps, Dominique (2002), "Generating functions for generating trees", Discrete Mathematics, 246 (1–3): 29–55, arXiv:math/0411250
Telephone number (mathematics)
Telephone_number_(mathematics)
Process of energy transfer to an object via force application through displacement
{\displaystyle W=\Delta E_{\text{k}}.} The work of forces generated by a potential function is known as potential energy and the forces are said to be
Work_(physics)
Feature of a system that is preserved under some transformation
}+K^{\mu }|x|^{2}-2K^{\nu }x_{\nu }x_{\mu },} with D generating scale transformations and K generating special conformal transformations. For example, N
Symmetry_(physics)
family of functions is built from translations and modulations of a generating function. In 1946, Dennis Gabor suggested the idea of using a granular system
Gabor_atom
Dynamic disturbance in a medium or field
There are two types of waves that are most commonly studied in classical physics: mechanical waves and electromagnetic waves. In a mechanical wave, stress
Wave
Mathematical function
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: ψ ( z ) = d d z ln Γ ( z ) = Γ ′ ( z ) Γ ( z )
Digamma_function
Symmetry of spatially mirrored systems
In physics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate. In three dimensions, it can also
Parity_(physics)
Theory of forces and subatomic particles
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions
Standard_Model
Transforming a function in such a way that it only takes a single argument
is the technique of translating a function that takes multiple arguments into a sequence of families of functions, each taking a single argument. In
Currying
Decomposition of an integer as a sum of positive integers
3010, 3718, 4565, 5604, ... (sequence A000041 in the OEIS). The generating function of p {\displaystyle p} is ∑ n = 0 ∞ p ( n ) q n = ∏ j = 1 ∞ ∑ i =
Integer_partition
Probabilistic optimization technique and metaheuristic
probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization
Simulated_annealing
Mathematical entity to describe the probability of each possible measurement on a system
In quantum physics, a quantum state is a mathematical entity that represents a physical system. Quantum mechanics specifies the construction, evolution
Quantum_state
Coordinate transformation that preserves the form of Hamilton's equations
canonical. The various generating functions and its properties tabulated below is discussed in detail: The type 1 generating function G1 depends only on the
Canonical_transformation
Computational quantum mechanical modelling method to investigate electronic structure
theory (DFT) is a computational quantum mechanical modeling method used in physics, chemistry and materials science to investigate the electronic structure
Density_functional_theory
Formulation of classical mechanics
{\displaystyle Q_{m}=\beta _{m}} . Setting the generating function equal to Hamilton's principal function, plus an arbitrary constant A {\displaystyle A}
Hamilton–Jacobi_equation
Generalization of the Meijer G-function and the Fox–Wright function
generalization of the Fox H-function was given by Ram Kishore Saxena. A further generalization of this function, useful in physics and statistics, was provided
Fox_H-function
Fundamental theorem in condensed matter physics
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves
Bloch's_theorem
Elementary particle involved with rest mass
Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model
Higgs_boson
Division of elementary particles
measurements. There are functions used to generalize terms for introduction in a new quark that is an isosinglet and is responsible for generating
Generation_(particle_physics)
Presence/absence of symmetry or correlation in a many-particle system
In physics, the terms order and disorder designate the presence or absence of some symmetry or correlation in a many-particle system.[citation needed]
Order_and_disorder
Eighteenth letter of the Greek alphabet
busy beaver function. In civil engineering, σ refers to the normal stress applied on a material or structure. In nuclear and particle physics, σ is used
Sigma
Mathematics concept
have been omitted from the standard textbooks on special functions in mathematical physics and in mathematics and have only a relatively scarce presence
Romanovski_polynomials
Creating a sequence of numbers that cannot be predicted
applications of randomness have led to the development of different methods for generating random data. Some of these have existed since ancient times, including
Random_number_generation
Physics phenomenon
entanglement is at the heart of the disparity between classical physics and quantum physics: entanglement is a primary feature of quantum mechanics not present
Quantum_entanglement
Applications of machine learning to quantum physics
it has incredibly high promise for more efficiently generating efficient optimization functions. Machine learning techniques can be used to find a better
Machine_learning_in_physics
Product of numbers from 1 to n
connects back to analytic combinatorics through the exponential generating function, which for a combinatorial class with n i {\displaystyle n_{i}} elements
Factorial
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GENERATING FUNCTION-PHYSICS
GENERATING FUNCTION-PHYSICS
GENERATING FUNCTION-PHYSICS
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