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...ulus]]. A summation equation compares to a [[difference equation]] as an [[integral equation]] compares to a [[differential equation]]. ...on%22+OR+%22summation+equation%22 Summation equations or discrete integral equations] ...

...thor1=Scott |first=Patricia |title=Applications of the Kirchhoff-Helmholtz integral to problems in seismology |date=1983 |author2=Helmberger |first2=Don |autho *[[Computational_aeroacoustics#Kirchhoff_integral|Kirchhoff integral]] ...

...tial equations named after Euler|List of things named after Leonhard Euler#Equations}} ...rd Euler]]. It is given by:<ref>Ince, E. L. "L. 1944 Ordinary Differential Equations." 227.</ref> ...

In [[mathematics]], '''Carleman's equation''' is a [[Fredholm integral equation]] of the first kind with a [[logarithmic kernel]]. Its solution w * A.D. Polyanin and A.V. Manzhirov, ''Handbook of Integral Equations'', CRC Press, Boca Raton, 1998. {{ISBN|0-8493-2876-4}} ...

...including the [[elementary function]]s and their repeated [[antiderivative|integral]]s. Liouvillian functions can be [[recursive definition|recursively defined ...garithm]] function does not need to be explicitly included since it is the integral of <math>1/x</math>. ...

{{Short description|Class of integral and differential operator}} ...d of [[harmonic analysis]], an '''oscillatory integral operator''' is an [[integral operator]] of the form ...

...ahn]]-Cigler ''q''-addition, the [[Jackson derivative]], and the [[Jackson integral]]. * Jackson, F. H. (1917). The <math>q</math>-integral analogous to Borel's integral. Messenger Math, 47, 57–64. ...

...named after [[Pierre Simon Laplace]] and [[John Renshaw Carson]], is an [[integral transform]] with significant applications in the field of [[physics]] and e ...nt, <math>i\infty</math> refers to the imaginary axis, which indicates the integral is carried out along a straight line parallel to the imaginary axis lying t ...

In mathematics, the '''Natural transform''' is an [[integral transform]] similar to the Laplace transform and Sumudu transform, introduc Khan<ref name="Khan"/> showed that the above integral converges to [[Laplace transform]] when ''u''&nbsp;=&nbsp;1, and into [[Sum ...

...approximate solutions of [[partial differential equations]] and [[integral equations]] based on the translates of [[sinc]] function and Cardinal function C(f,h) *approximate definite and indefinite [[integral|integration]], ...

{{Short description|Integral transform introduced in 1990}} ...93 |title=Sumudu transform: a new integral transform to solve differential equations and control engineering problems |url=http://www.tandfonline.com/doi/abs/10 ...

{{Short description|Integral inequality}} ...emma of Bellman and its application to uniqueness problems of differential equations | author = I. Bihari | journal = [[Acta Mathematica Hungarica]] |date=March ...

{{calculus|expanded=integral}} ...s]], [[Euler's formula]] for [[complex number]]s may be used to evaluate [[integral]]s involving [[trigonometric functions]]. Using Euler's formula, any trigon ...

{{Short description|Change of time of the value of an integral}} ...of a [[volume integral|volume]] or [[surface integral]] whose domain of [[integral|integration]], as well as the [[integrand]], are [[Function (mathematics)|f ...

...iption|One of two formulae that are used in the resolution of Diophantine equations}} The identities are used in translating Diophantine problems connected with integral points on [[hyperelliptic curve]]s into [[S-unit equation]]s. ...

...annes Jisse |last1=Duistermaat |first2=Lars |last2=Hörmander|title=Fourier integral operators. II|volume=128 |series=Acta Mathematica|publisher=Institut Mittag ...annes Jisse |last1=Duistermaat |first2=Lars |last2=Hörmander|title=Fourier integral operators. II|volume=128 |series=Acta Mathematica|publisher=Institut Mittag ...

Where the new parameter <math>w</math> defines the integral bound of the '''upper-incomplete form''' and '''lower-incomplete form''' of ==Differential equations== ...

...c{1}{1+x}</math> to all positive real <math>x</math> leads to a convergent integral for the summation: where ''E''₁(''z'') is the [[exponential integral]]. This is by definition the [[Borel sum]] of the series, and is equal to t ...

In mathematics, '''Jacobi transform''' is an [[integral transform]] named after the mathematician [[Carl Gustav Jacob Jacobi]], whi ...3 (1963): 113-120.</ref><ref>Debnath, L. "SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS BY JACOBI TRANSFORM." BULLETIN OF THE CALCUTTA MATHEMATICAL SOCIETY 59.3-4 ...

...ong ground motion|ground motion]].<ref>{{cite journal|title=New predictive equations for Arias intensity from crustal earthquakes in New Zea |journal=Journal of It is defined as the time-[[integral]] of the square of the [[ground acceleration]]: ...