# An Etymological Dictionary of Astronomy and AstrophysicsEnglish-French-Persian

## فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

### M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 14 Search : integral
 definite integral   درستال ِ هدارمند   dorostâl-e hedârmandFr.: intégrale définie   An integral with upper and lower limits.→ definite; → integral. differential and integral calculus   افماریک ِ دگرسانه‌ای و درستالی   afmârik-e degarsâne-yi va dorostâliFr.: calcul différentiel et intégral   The two branches of mathematics that make up the → calculus. → differential calculus; → integral calculus.→ differential; → integral; → calculus. double integral   درستال ِ دوتایی   dorostâl-e dotâyiFr.: intégrale double   The simplest case of a → multiple integral.→ double; → integral. Fourier integral   درستال ِ فوریه   dorostâl-e FourierFr.: intégrale de Fourier   An integral used in the → Fourier transform.→ Fourier analysis; → integral. Fresnel integrals   درستال‌های ِ فرنل   dorostâlhâ-ye FresnelFr.: intégrales de Fresnel   Two integrals that involve quadratic equations in the sine and cosine functions and are defined as: C(x) = ∫ cos (πt2/2) dt and C(y) = ∫ sin (πt2/2) dt, integrated from 0 to x. They are quite frequently used in optics studying → Fresnel diffraction and similar topics. The Fresnel integrals are also used in railway and freeway constructions. These integrals may be evaluated to arbitrary precision using → power series. Alternatively the amplitudes may be found graphically by use of → Cornu's spiral. indefinite integral   دُرُستال ِ ناهدارمند   dorostâl-e nâhedârmandFr.: intégrale indéfinie   Math.: An integral without upper and lower limits. The general antiderivative of a function. → definite integral.→ definite; → integral. integral   ۱) درست؛ ۲) دُرُستال   1) dorost; 2) dorostâlFr.: 1) intégral; 2) intégrale   1) Consisting of whole numbers or integers. 2) Mathematical function obtained by the process of → integration.Integral, from M.Fr. intégral, from M.L. integralis "forming a whole," → integer "whole."1) Dorostâl, from dorost "whole, complete; healthy; right," related to dorud "benediction, praise, thanksgiving," from Mid.Pers. drust "whole; healthy; well, right," drôd "health, thriving;" O.Pers. duruva- "firm, certain, immune;" Av. druua- "healthy;" cf. Skt. dhruvá- "fixed, firm, immovable, lasting, certain;" Russ. zdorovyjj "healthy;" See also → sound. 2) Dorostâl, from dorost + -âl, → -al. integral calculus   افماریک ِ دُرُستالی   afmârik-e dorostâliFr.: calcul intégral   Branch of the calculus that deals with integration and its use in finding volumes, areas, equations of curves, solutions of differential equations, etc.→ integral; → calculus. integral equation   هموگش ِ دُرُستالی   hamugeš-e dorostâliFr.: équation intégrale   An equation involving an unknown function that appears as part of an integrand.→ integral; → equation. integral field spectroscopy   بیناب‌نمایی ِ درست ِ میدان   binâbnemâyi-ye dorost-e meydânFr.: spectroscopie intégrale de champ   A technique in spectroscopy for recording a spectrum from each point of an extended object. The field of view image is divided into a multitude of small components using different methods, e.g. lenslet arrays, fiber bundles, or image slicers. From each component a spectrum is extracted or an image is reconstructed at a particular wavelength.→ integral; → field; → spectroscopy. integral function   کریای ِ دُرُستالی   karyâ-ye dorostâliFr.: fonction intégrale   A function whose image is a subset of the integers, i.e. that takes only integer values.→ integral; → function. integral operator   آپارگر ِ دُرُستالی   âpârgar-e dorostâliFr.: opérateur intégral   Math.: An operator whose inverse is a differential operator.→ integral; → operator. Jacobi integral   درستال ِ یاکوبی   dorostâl-e JacobiFr.: intégrale de Jacobi   The integral admitted by the equations of a body of infinitesimal mass moving under the → gravitational attractions of two massive bodies, which move in circles about their → center of gravity. The Jacobi integral is the only known conserved quantity for the circular → restricted three-body problem. In the co-rotating system it is expressed by the equation: (1/2) (x·2 + y·2 + z·2) = U - CJ, where the dotted coordinates represent velocities, U is potential energy, and CJ the constant of integration (→ zero-velocity surface). The Jacobi integral has been used for two different purposes: 1) to construct surfaces of zero velocity which limit the regions of space in which the small body, under given initial conditions, can move, and 2) to derive a criterion (→ Tisserand's parameter) for re-identification of a → comet whose orbit has suffered severe perturbations by a planet. Also known as Jacobi constant.Named after Karl Gustav Jacobi (1804-1851), a German mathematician who did important work on elliptic functions, partial differential equations, and mechanics; → integral. multiple integral   درستال ِ بستایی   dorostâl-e bastâyiFr.: intégrale multiple   A series of successive integrations in which the integral operator acts on the result of preceding integration.→ multiple; → integral.