In mathematics, auxiliary functions are an important construction in transcendental number theory. They are functions that appear in most proofs in this...

attitude of the unconscious. Later in the book, Jung describes the auxiliary function as being capable of some significant development or differentiation...

\mathbb {C} } . The Jacobi theta function defined above is sometimes considered along with three auxiliary theta functions, in which case it is written with...

person's most preferred extraverted function, which is the dominant function for extraverted types and the auxiliary function for introverted types. Jung hypothesized...

throughout the proof. The main idea of Baker's proof is to construct an auxiliary function Φ ( z 1 , … , z n − 1 ) {\displaystyle \Phi (z_{1},\ldots ,z_{n-1})}...

The Mayer f-function is an auxiliary function that often appears in the series expansion of thermodynamic quantities related to classical many-particle...

In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one...

Euler's identity. This work centred on use of the so-called auxiliary function. These are functions which typically have many zeros at the points under consideration...

grammatical behavior, as described below. In some cases, verbs that function similarly to auxiliaries, but are not considered full members of that class (perhaps...

values by evaluating an auxiliary function on the preceding values. The limit is thus a fixed point of the auxiliary function, which is chosen for having...

Trigonometric integrals can be understood in terms of the so-called "auxiliary functions" f ( x ) ≡ ∫ 0 ∞ sin ⁡ ( t ) t + x d t = ∫ 0 ∞ e − x t t 2 + 1 d...

To incorporate these conditions into one equation, we introduce an auxiliary function L ( x , y , λ ) ≡ f ( x , y ) + λ ⋅ g ( x , y ) , {\displaystyle {\mathcal...

nested functions, the auxiliary function can be nested inside the wrapper function and use a shared scope. In the absence of nested functions, auxiliary functions...

Auxiliary polynomial is a term in mathematics which may refer to: The auxiliary function argument in transcendence theory The characteristic polynomial...

In stereochemistry, a chiral auxiliary is a stereogenic group or unit that is temporarily incorporated into an organic compound in order to control the...

function C(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D Plot of the Fresnel auxiliary function...

thus, for a complicated function, the determination of the domain passes through the computation of the zeros of auxiliary functions. Similarly, if square...

these languages heavily use auxiliary functions called thunks to compute the argument values, and memoize these functions to avoid repeated calculations...

dominant function is supported by two auxiliary functions. (In MBTI publications the first auxiliary is usually called the auxiliary or secondary function and...

program used by technical writers to create online help systems. The basic functions of a Help Authoring Tool (HAT) can be divided into the following categories:...

mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for...

four main functions of consciousness: two perceiving or non-rational functions (Sensation and Intuition), and two judging or rational functions (Thinking...

support functions or performing certain duties such as garrison troops, usually on a part-time basis. Unlike a military reserve force, an auxiliary force...

In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-defined...

of "verbs in auxiliary function" that "In contrast to full [i.e. lexical] verbs, [these verbs] are capable of functioning as auxiliary or 'helping' verbs...

or shadow vessel, are specialized ships which provide support and auxiliary functions for large sailing and motor yachts. In general yacht support vessel...

startup and synchronize the turbine to the electrical grid, and other auxiliary functions. The plant was completed in four phases and covers an area of over...

corresponding virial expansions. The auxiliary function y ( r ) {\displaystyle y(r)} is known as the cavity distribution function.: Table 4.1  It has been shown...

In linear algebra, a sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm or a Banach functional...

the partition function in quantum field theory. A common, useful modification to the partition function is to introduce auxiliary functions. This allows...