function (fungkshon)

[ And all the ceremony of this compact Seal'd in my function , by my testimony. Shak., T. N., v. 1. IMG:content-1942.png:[blocks in formation] Function carries pleasure with it as its psychical accompaniment, but what determines, makes, and is good or bad, is in the end function . F. H. Bradley, Ethical Studies, p. 123. 3. Power of acting; faculty; that power of acting in a specific way which appertains to a thing by virtue of its special constitution; that mode of action or operation which is proper to any organ, faculty, office, structure, etc. (This is the most usual signification of the term.] Dark night, that from the eye his function takes, The ear more quick of apprehension makes. Shak., M. N. D., iii. 2. So slow th' unprofitable moments roll, That lock up all the functions of my soul. Pope , Imit. of Horace, I. i. 40. I think, articulate, I laugh and weep, And exercise all functions of a man. Cowper , Task, iii. 199. Functions dwell in beast and bird that sway The reasoning mind, or with the fancy play. Words worth, Humanity. service with elaborate ritual and music. I... kept fasts and feasts innumerable, Matins and vespers, functions to no end. Browning, Ring and Book, I. 212. On the whole, the music was good, and the function sufficiently impre ive - what with the gloom of the temple everywhere starred with tapers, and the grand altar lighted to the mountain-top. W. D. Howells, Venetian Life, xviii. (b) Any important occasion marked by elaborate ceremonial: extended in recent use to cover social entertainments, as operas, balls, and receptions. The other great annual function is the burning of Guy Fawkes on the 5th of November. Fortnightly Rev., N. S., XXXIX. 181. On the first occasion when Robert could be induced to attend one of these functions [breakfast-parties], he saw opposite to him what he supposed to be a lad of twenty. Mrs. Ward, Robert Elsmere, xxxiii. 6. In math., a mathematical quantity whose value depends upon the values of other quantities, called the arguments or independent variables of the function; a mathematical quantity whose changes of value depend on those of other quantities called its variables. Thus, if the diameter of a circle be conceived to vary in length, the length of the circumference will also vary with it, in accordance with a fixed geometrical law, and is therefore a function of the diameter, the latter being regarded as the independent variable. So in the equation y = ax + b, if x be conceived to vary independently, y will be its function, since its value will vary with each succe ive value of x. The common algebraic notation is y = f ( x ), to be read "y is a function of x." F, 4, and other letters are often used in place of f. It is not the special value of fx, but this quantity considered as variable and as depending upon z, which is called the function. It is even called the same function irrespective of the special values of certain parameters upon which it may depend, and which are considered not as variables, but as constants. The earlier analysts used function to mean merely a power, or continued product of a quantity into itself. The present mathematical meaning first appears in the Latin correspondence between Leibnitz and John Bernoulli. Mathematical usage is not precisely settled as to the meaning, and this in two respects. First, as some writers use the word, the po ible values of the function depend upon the values of the variables; so that, if y is a function of z, there must be some value which y can take for some value of z, which it cannot take for some other value of x. But other writers hold that two quantities which are functions of a third are functions of each other. For example, if x = tant and y = tan (t2) + i tan ( ty 3), they hold that y is a function of x, although it can take every value for every value of x; for there is even here a connection between the values of x and y, so that in the course of any continuous change of a the mode of change of y is somewhat restricted. Secondly, according to the usage of Cauchy and his followers, if an imaginary quantity, X + Yi, be so connected with another, x + yi, that X and Y are each of them functions of x and y, say X = F ( x, y) and Y = f ( x, y), then the former imaginary is a function of the other; but the majority of mathematicians have restricted the name function to what the school of Cauchy would term monogenous and differentiable functions, although such a restriction is impo ible where the variable does not vary continuously. The tendency of recent writ tion of the term. ers is to give the greatest po ible breadth to the applica7. Hence, anything which is dependent for its value, significance, etc., upon something else. Abelian function. See Abelian2. Adjunct spherical function, a higher differential coefficient of one of the spherical functions Pn or Qn multiplied by certain constants depending on m and n and by (1-x2)m/2, where the distribution of electricity upon a cone. - Conjugate functions, two functions, u, v, of rectangular coördinates, x, y, such that u + v - 1 is a monogenous function of x+y-1.- Continuous, critical, curvital, etc., function. See the adjectives. - Cyclic function, a function of more than one variable which experiences a constant addition to its value every time the variables are made to vary continuously from a given set of values through some cycle of values back to the same primitive set of values. Thomson and Tait. - Cyclotomic function, an irreducible function forming a divisor of an equation for the division of the circle into a number of equal parts. Cylindrical function, a Be elian function of the first or second order. [So first called by Heine, on account of the connection of these functions with the potential of a cylinder.]- Derivative function. See derivative.Derived function, a differential coefficient. - Differentiable function, a function having a determinate finite differential coefficient for every value of the variable within a certain limit. Du Bois - Reymond, 1874. See We i ers tra i an function (b), under We i ers tra i an. Dihedral function. See polyhedral function, under polyhedral. Dir ich let i an function, a function occurring in the theory of the numbers of cla es of binary quadratic forms. It is represented by the expre ion Σ 1 except when D=1 (mod. 4), when this expre ion is to be divided by D2-11 1-(-1) 8 () ns 28. In this expre ion () is the Legen drian symbol in its Jacob i an sense, and the summation extends to all values of n which are positive, integer, and relatively prime to 2D. - Discontinuous function. See dis continuous, 3. - Di ipation or di ipative function, di ipativity; half the rate at which the energy of a system is di ipated by forces like viscosity, etc. It forms one of the terms of the Lag rangi an function. - Distributive function. See distributive. - Doubly periodic functions, functions which return to the same values when the variable is increased by either one of two values the ratio of which is imaginary. Elliptic function. See elliptic.-Entire or integral function, or rational and integral function, a function which is expre ible as a polynomial or infinite series containing only positive integral powers of its variable. Equivalence of functions, a communistic term implying that no man's labor ought to be remunerated at a higher rate than that of any other man, whatever be the difference of capacity or production. - Euler's function, the simplest function which becomes 1n-2n + 3n (2x1)n, when z is a positive integer and vanishes for x = 0.et. This is not to be confounded with the Eulerian function, for which see the adjective. - Even function, a function whose value is not changed by reversing the sign of the variable. - Explicit, exponential, fluctuating, etc., function. See the adjectives. - Factorial function, an integral function which can be put in the form ( x - a ) (x-b) (x-c), etc., where a, b, c, etc., are in arithmetical progre ion.- Force function, the function expre ing the potential of a force. See force - function. - Fractionary function. Same as meromorphic function. This is the older phrase, and is still preferred by some writers.Fuchsian function, a one-valued function which remains unaltered by the transformations of a Fuchsian group, and in the interior of a certain curvilinear polygon has the same value only for a finite number of values of the variable. Function of judgment, in the Kantian philos., the particular mode of judging which determines a particular logical form of proposition, as universal, particular, or singular in quantity; affirmative, negative, or infinitated in quality; categorical, conditional, or disjunctive in relation; a ertory, problematic, or apodictic in modality. Function of limited domain, a lacunary function.-Function of limited variation, a function such that the sum, without regard to signs of all its changes of value between given values of the variable, is finite.Gamma function. See gamma. - Gau ian function, the same as the hypergeometric function of the second order. Generating function, a function which, when developed according to powers of its variable, gives as function the coefficients of the succe ive terms the succe ive values of a discrete function. Thus, et is the generating function of 1.2.3.4. 1 n' 1 because e=1+1+2+3+, etc. Goniometric function, one of the six quotients of two sides of an oblique triangle considered as a function of two of the angles. - Graphometric function. See grapho metric. Gudermannian function. See Gudermannian. - Hamilton i an functions, a series of functions introduced into dynamics by Sir William R. Hamilton, any one of which may be used instead of the Lag rangi an function. The common Hamilton i an function expre es the sum of the kinetic and positional energy. - Hankel's function, the function fx=2n (1/n)/En [1/n* $ (sin nmx)], 1 where s> 1, and where =0 for y=0, y=1, y=-1, while y=1 for all other values of the variable. Harmonic, holomorphic, etc., function, See the adjectives.Heine's function, the function Ω(x, a) = c In [(1 - e2na)/(1-e2n+x)a). 1 Homogeneous function, an algebraic polynomial in two variables, all the terms being of the same degree, - Hyper abelian function. See hyper abelian. -Hyperbolic function. (a) A Gudermannian function. (6) One of several functions related to 1+ k2 sinh3 & in the same manner in which ordinary elliptic functions are re lated to y1-k2 sin2 6, being merely transformed elliptic functions. Hyper distributive, hyper elliptic, hyperfuchsian, hyper spherical, etc., function. See the adjectives. Icosahedral function. See polyhedral. Illegitimate function, one which follows one law for some values of the variables and another for others. Implicit function, one which is defined by an equation of which the function does not form one member. - Integrable function, a function such that, if the integral between two values of the variable be divided into infinitesimal parts, and each of these be multiplied by the maximum value of the function, then the sum of the products has a determinate value irrespective of the mode of separation of the interval into infinitesimal parts, so that the function has a determinate integral. Integral function, a holomorphic function: but with some writers an algebraic polynomial is meant. See entire function.Intermediary function. See intermediary. - Interpolary function, a kind of function used in interpolation. - Irrational function, a function which cannot be expre ed as the ratio of two algebraic polynomials in its variables. Irreducible function, a function u connected with its variables, x, y, etc., by an equation F ( z, y, etc., u) = 0, which cannot be separated into indepen dent factors. For example, y = Vz is an irreducible funetion, for (y2- x ) = 0 can be separated only into the factors (y + √x) (y - Va ), which have no general meaning independent of each other. If the Riemann's surface of an irreducible function consists of several sheets, these are all connected; and this may be taken as the definition.Irreproductive function, a reproductive function of order zero. Iterative function. See iterative.-Jacob i an function, one of the functions O, H, etc., em. ployed by Jacobi as subsidiary to the study of elliptic functions. J function, the Be elian function of the first kind. Keplerian function, a function expre ed by an equation similar to that of Kepler's problem. - Lacunary function. See lacunary. - Lag rangi an function, the kinetic diminished by the positional energy, or by what corresponds to the positional energy in the case of variable forces. Lamé's function, a kind of Laplace's funetion in which the three direction cosines enter instead of the radius vector, latitude, and longitude. - Laplace's function, spherical function, or spherical harmonic, a function of two variables analogous to a trigonometrical series, used to expre the distribution of any continuous quantity over a surface. A Laplace's function of the ath order is any function Yn of the two variables and 4, which satisfies the differential equation 1 2 Dμ{(1-2) Dm Xn}+ Yn +12 D Yn + n (n + 1) Yn = 0. See equation of Laplace's functions, under equation. - Legendrian function, one of the xn functions of spherical harmonics.-Limited function, one which has a maximum and a minimum value within some finite interval of the variable. - Long i metric function. See long i metric. -Major function, a certain function used in the theory of Abelian functions. - Meromorphic, metabatic, modular, mono dromic or mono tropic, monogenous, monotonous, multiform function. See the adjectives. Non-uniform function. Same as multiform function. - Normal function, a spherical harmonic of a higher order. - Numerical generating function, the generating function showing the number of a syzygetic invariants of each deg order. Octahedral function. See polyhedral. Odd function, one which changes its sign with the variable. One-valued function, one which has only one value for each set of values of the variables. - Order of a function, the order of the algebraic differential equation of lowest order which connects the function with its variable.-Ordinary function, a differentiable function which in reference to no axis of absci as po e es an infinite number of maxima. Partitively continuous, differentiable, etc., function, a function such that the interval of the variable considered may be so divided into parts that the function is continuous, differentiable, etc., in each part.-Periodic function. (a) As ordinarily understood, a function which, whenever the variable is increased by a certain constant, called the period, has its value unchanged. (b) In a generalized sense, a function which has its value unchanged by the substitution for its variable of a certain algebraic function thereof. A periodic function of the second kind is one for which this function is linear. Perturbative function. See perturbative. Picard's functions, hyper geometrical functions of two variables. - Plane or planimetric function, a function expre ing one of the relations between the areas of the three triangles formed by joining a variable point in a plane to the vertices of a fundamental triangle. Pn function, the Legendre's coefficient of the nth order, the coefficient of an 2408 in the development of (1-2ax + a2)- according to ascending powers of a. - Poly dromic or poly tropic function, one which is not mono tropic. - Polyhedral function. See polyhedral. Potential function, the fune tion expre ing the potential of attractions upon a particle. Principal function, the time-integral of the Lag rangi an function. - On function, a harmonic function such that 1(y-2) = 2n (2n + 1) Qn (3) Pn (x). Quasi-periodic function, a function which returns to its value multiplied by a constant when the variable is in fund expre ion in Abelian functions having one characteristic, Radical function, a rational, integral, and homogeneous -Rational and integral function. See entire function. Rational function, a function whose value in terms of the variable is expre ible as a rational fraction.Reciprocal functions, a pair of functions f and f-1, so related to each other that if y is one of the values of fr, then z is one of the values of f-ly, and conversely. Each function is also said to be the reciprocal of the other. The term converse would be preferable. Representative function. See representative. - Reproductive function of order function such that, for a stante, the equation holds f( x )=f(x). Riemann's function, a function satisfying the differential equation of the hyper geometrical series, and defined by Riemann by means of the properties of its critical points. It is denoted by P. Rosenhain's function, an ultra-elliptic function of the first kind.-Scalar function, a real numerical quantity having one or more values for each point of three dimensional space. - Sigma function, See sigma. - Similar functions. (a) Functions which admit the same substitutions. (b) Two physical quantities whose several mathematical relations to two other physical quantities are the same. - Sinusoidal function, a simple harmonic, - Spherical function. See Laplace's function. Stereometric function, a ratio of two of the tetrahedrons formed by joining a variable point in space to the four summits of a fixed tetrahedron.--Striped function, a function which is represented by a pattern in stripes.-Sturmian function. See Sturmian. - Suppositionle function, a function subject to no general condition whatever - which may, for instance, be either limited or unlimited. Symmetric function, a function of several variables whose value is never altered by interchanging the values of any two of the variables. Synectic function. See synectic. - Tetrahedral function. See poly hedral. - Theory of functions, a branch of mathematics which concerns the general properties of different general forms of functions. It is sometimes regarded as embracing the entire theory of the higher functions, such as the gamma function, spherical harmonics, elliptic functions, etc. Thermodynamic function, the amount of heat which a body will give out in being brought to a standard pre ure and temperature. - Theta function. See theta, -Toroidal function, a function serving to expre the potential of an anchor-ring.-- Transcendental function, any function not algebraic. Trigonometrical functions. See trigonometrical. - Uniform function, a function such that its variable, while remaining within given limits, cannot pa through a cycle of values so as to return to its original value without the function also returning to its original value. - Unlimited function, a function which within every interval has values greater than any predesignate finite limit and other values le than any predesignate finite limit. For example, suppose that y=0 when a is irrational, while y = (1)Pq when z is equal to the irreducible fraction p / q. Then, although y never becomes infinite, yet between any two a ignable values of x it has values greater than any predesignate positive number, and values le than any predesignate negative number. Vector function, a quantity of the nature of a vector, having magnitude and direction, distributed through space so as to have a definite magnitude and direction at each point. - Velocity function, in hy drodynamics, a scalar function whose partial differential coefficient for a linear displacement of the variable point is equal to the component velocity of the fluid in that direction at that point. - Vital functions, functions immediately nece ary to life, as those of the brain, heart, and lungs. We i ers tra i an function. See Weierstras sian.-Xn function, a Legendrian polynomial of the ath order, or function of the latitude and longitude on a sphere, satisfying Laplace's equation. In function, the Laplace's ath coefficient, being what Pn becomes when for the variable x we substitute x = cos e cos 01 + sin e sin 01 cos (-1). - Zeta function. See zeta. [ function (fungk's hon), v. i. To perform a function; work; act; functionate; especially, in physiol., to have a function; do or be something physiologically. It seems probable that the policy here given formed the ground of an action in the Insurance Court created by the statute of Elizabeth,. which functioned till towards the end of the seventeenth century. F. Martin, Hist. of Lloyd's, p. 48. The endodermal sac forms the axis of the tentaculocyst, its cells secrete crystalline concretions, and it functions as an otocyst. E. R. Lankester , Encyc. Brit., XII. 551.