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	Exponential integral -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, the exponential integral Ei(x) is defined as
		The exponential integral is closely related to the (Click link for more info and facts about logarithmic integral function) logarithmic integral function li(x),
		This function may be regarded as extending the exponential integral to the
	www.absoluteastronomy.com /encyclopedia/e/ex/exponential_integral.htm (213 words)

	List of mathematical functions Article, Listmathematicalfunctions Information (Site not responding. Last check: 2007-10-08)
		Exponential function : raise a fixed number to avariable power.
		Logarithm : the inverses of exponential functions; useful to solve equationsinvolving exponentials.
		Logarithmic integral : Integral of the reciprocal of thelogarithm, important in the prime number theorem.
	www.anoca.org /function/number/list_of_mathematical_functions.html (497 words)

	Differentiation and integration of log and exponential functions
		Integral of the exponential of a linear factor
		Integral of the exponential of a radical factor
		Integral of the quotient of sums of exponentials
	www.jtaylor1142001.net /calcjat/Contents/CLogExp.htm (220 words)

	SLATEC (Site not responding. Last check: 2007-10-08)
		Exponential, logarithmic ALNREL-S Evaluate ln(1+X) accurate in the sense of relative error.
		Integrals of Bessel functions BSKIN-S Compute repeated integrals of the K-zero Bessel function.
		Elliptic integrals RC-S Calculate an approximation to DRC-D RC(X,Y) = Integral from zero to infinity of -1/2 -1 (1/2)(t+X) (t+Y) dt, where X is nonnegative and Y is positive.
	www.glue.umd.edu /~NSW/ench250/slatec.htm (13659 words)

	[No title]
		Course (catalog) Description: This is the first course in calculus and analytic geometry focusing on limits, continuity, derivatives, and indefinite and definite integral, differentiation and integration of exponential functions, logarithmic functions and their applications.
		Evaluate derivatives and integral of exponential functions, logarithmic functions and their applications.
		The Definite Integral a) Antiderivatives (indefinite integral) b) Sums and sigma notation c) Definition and properties of the definite integral d) The Fundamental Theorem of Calculus e) Evaluation of integral by the substitution method f) Area under a curve g) Numerical integration 6.
	www.oakton.edu /acad/dept/mpcs/cs/pict/mat/syl/m250.syl (607 words)

	Leonid Tolmatz
		Asymptotics of the distribution of the integral of the positive part of the Brownian bridge for large arguments.
		Asymptotics of the distribution of the integral of the exponential (geometric) Brownian motion for large arguments with application to Asian options.
		On tabulation of the distribution of the integral of the exponential (geometric) Brownian motion.
	www.tolmatz.net (224 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Elliptic integrals RC-S Calculate a double precision approximation to DRC-D DRC(X,Y) = Integral from zero to infinity of -1/2 -1 (1/2)(t+X) (t+Y) dt, where X is nonnegative and Y is positive.
		QC25S-S To compute I = Integral of F*W over (BL,BR), with error DQC25S-D estimate, where the weight function W has a singular behaviour of ALGEBRAICO-LOGARITHMIC type at the points A and/or B. (BL,BR) is a part of (A,B).
		2 I. Differential and integral equations I. Differential and integral equations I1.
	www-acs.ucsd.edu /offerings/userhelp/COLD/slatec.toc.defunct (9461 words)

	Math 134, Summary of Test #3 Lectures (Site not responding. Last check: 2007-10-08)
		Improper integrals are so named since they involve intervals which are infinite in extent.
		The probability of an event is a number between 0 and 1 that represents that chances of the event occurring.
		This means that it is more likely for the value of x to be "small" than it is for it to be large, since f(x) is a decreasing function.
	www.math.uiuc.edu /~dcmurphy/math134/summary3.html (2323 words)

	Untitled Document - Exponential Integrals (Site not responding. Last check: 2007-10-08)
		Information on the exponential integrals can be found in Abramowitz & Stegun, Chapter 5.
		These routines compute the exponential integral E_i(x), where PV denotes the principal value of the integral.
		These routines compute the exponential integral Ei_3(x) = \int_0^x dt \exp(-t^3) for @c{$x \ge 0$} x >= 0.
	www.ugcs.caltech.edu /info/gsl/specfunc_17.html (158 words)

	math151 - Catalog Information
		It enables us to define slope of curves, to calculate velocities, accelerations of moving bodies and to predict the times when planets would be closest together or farthest apart.
		Integral calculus deals with the problem of determining a function from information about its rate of change.
		It enables us to calculate the future location of a body from its present position, to find the areas of irregular regions in the plane, to measure the lengths of curves, and to find the volumes and masses of arbitrary solids.
	www.math.metu.edu.tr /WWW/courses/math151cat.html (348 words)

	Week 3 Tutorial Lab
		The reason that the exponentiation has the dot before the carat is that this function will handle vector inputs. Check this with the following commands.
		Again, take some time to notice each part of the function script. There is the first line that specifies that this is a function and gives the name of the function. It also specifies the inputs and outputs.
		Matlab has a built-in function that computes the exponential integral function to full precision and it is called expint().
	www.cs.wisc.edu /~hasti/cs310/indivLab/MatProg3/MatProg3IndivLab.html (1066 words)

	[No title]
		The exponential integral function is defined by $Ei(z)=-\int_{-z}^{\infty} \frac{e^{-t}}{t}dt$, where the principal value is taken.
		The hyperbolic sine integral is defined by $Shi(z)=\int_{0}^{z} \frac{sinht}{t} dt$.
		The Clausen integral is defined as $f(\theta)=-\int_{0}^{\theta}ln(2sin\frac{t}{2})dt =\sum_{k=1}^{\infty}\frac{sink\theta}{k^2}$ $(0 \leq \theta \leq \pi)$.
	www.csd.uwo.ca /faculty/watt/home/research/openmath/spfun1.ocd (3083 words)

	Octave Functions: E (Site not responding. Last check: 2007-10-08)
		The eigenvalues (and eigenvectors) of a matrix are computed in a several step process which begins with a Hessenberg decomposition, followed by a Schur decomposition, from which the eigenvalues are apparent.
		Return an R by C matrix of random samples from the exponential distribution with parameter LAMBDA, which must be a scalar or of size R by C. exprel [math]
		These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2.
	octave.sourceforge.net /index/E.html (691 words)

	[No title]
		This is an easier integral to analyze because only the path of integration depends on z.
		Thus, g(z) = C + integral from 1/z to 1 of (exp(-u)/u du).
		This is closely akin to the exponential integral function Ei(z) = -integral_{-z}^infinity exp(-t)dt / t (1) where we take the principal value of this integral to deal with the singularity at t = 0.
	www.math.niu.edu /~rusin/known-math/00_incoming/divseq (882 words)

	Miscellaneous Functions
		Some books define the exponential integral of order 1 as the exponential integral:
		The sine and cosine integrals are defined as:
		The Fresnel sine and cosine integrals are defined as:
	www.efunda.com /math/miscellaneousfun/miscellaneousfun.cfm (62 words)

	Handbook of Mathematical Functions (Online), p. 227
		Exponential Integral and Related Functions WALTER GAUTSCHI AND WILLIAM F. Con tents Mathematical Properties.
		Exponential Integrals E,(z) for Large Arguments (2 5 s 5 m).
		Exponential Integral for Complex Arguments (I zI <29).
	www.convertit.com /Go/A101/Reference/AMS55.ASP?Res=150&Page=227 (275 words)

	Cubic Exponential Integral
		= 0 and where the integral is defined from 0 to x">
		is a variable or a parameter (depending on what is) where the computed cubic exponential integral values are stored;
		= Compute the exponential integral of order N. = Compute the principal value of the exponential integral.
	www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/exp3.htm (103 words)

	Extended precision special functions library
		* The integral is evaluated by either a power series or * continued fraction expansion, depending on the relative * values of a and x.
		* * This is accomplished using the inverse beta integral * function and the relations * * z = incbi(df2/2, df1/2, p) * x = df2 (1-z) / (df1 z).
		(b) - * 0 * * The incomplete gamma integral is used, according to the * relation * * y = igam(b, ax).
	www.netlib.org /cephes/qlibdoc.html (5763 words)

	Special Functions
		Thus, for example, integral representations of functions are valid only when the integral exists, but the functions themselves can usually be defined elsewhere by analytic continuation.
		Polylogarithm functions appear in Feynman diagram integrals in elementary particle physics, as well as in algebraic K-theory.
		The amplitude is exponentially damped in the classically inaccessible region on the right.
	documents.wolfram.com /v4/MainBook/3.2.10.html (1396 words)

	Bibliography
		A portable Fortran subroutine for exponential integrals of a complex argument, ACM Trans.
		Hyperelliptic integrals and the surface measure of ellipsoids, ACM Trans.
		Gastmans and W. Troost, On the evaluation of polylogarithmic integrals, Simon Stevin 55 (1981), 205-219.
	math.nist.gov /mcsd/Reports/2001/nesf/node38.html (8398 words)

	Exponential Function (Site not responding. Last check: 2007-10-08)
		As x becomes negative the curve flattens out against the x axis, just as the log curve approached the y axis.
		As x becomes positive the exponential function rises to infinity.
		The exponential of x is written exp(x), or sometimes E
	www.mathreference.com /ca-int,exp.html (115 words)

	The Incomplete Gamma Functions Since Tricomi - Gautschi (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		4 Chebyshev approximations for the exponential integral Ei (context) - Cody, Thacher - 1969
		3 A numerical method for generalized exponential integrals (context) - Chiccoli, Lorenzutta et al.
		3 the evaluation of generalized exponential integrals E (context) - Chiccoli, Lorenzutta et al.
	citeseer.ist.psu.edu /gautschi98incomplete.html (799 words)

	MATH 1080 #12: INTEGRAL OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS (Site not responding. Last check: 2007-10-08)
		Now you are going to do integrals for the exponential and logarithmic functions using the chain rule.
		The exponential function is the easiest because it is usually obvious.
		If the problem has an exponential function in it, try and fit it to the exponential form.
	www-math.cudenver.edu /~rbyrne/online/1080/108w12.htm (181 words)

	dexint.f (Site not responding. Last check: 2007-10-08)
		The C exponential integral is defined by C C E(N,X)=integral on (1,infinity) of EXP(-XT)/T**N C C where X=0.0 and N=1 cannot occur simultaneously.
		C M number of exponential integrals in the sequence, C M.GE.
		C D. Amos, Computation of exponential integrals, ACM C Transactions on Mathematical Software 6, (1980), C pp.
	www.cs.yorku.ca /~roumani/fortran/slatecAPI/dexint.f.html (510 words)

	Tables of Integrals, Series, and Products
		Integrals that can be reduced to elliptic or pseudo-elliptic integrals
		The hyperbolic sine integral shi(x) and the hyperbolic cosine integral chi(x)
		The sine integral and the cosine integral: si(x) and ci(x)
	www.mathtable.com /gr/gr6_toc (1010 words)

	SLATEC Keylist Index
		Evaluate the definite integral of a piecewise cubic Hermite function over an interval whose endpoints are data points.
		Calculate a double precision approximation to DRC(X,Y) = Integral from zero to infinity of -1/2 -1 (1/2)(t+X) (t+Y) dt, where X is nonnegative and Y is positive.
		Calculate an approximation to RC(X,Y) = Integral from zero to infinity of -1/2 -1 (1/2)(t+X) (t+Y) dt, where X is nonnegative and Y is positive.
	www.cs.yorku.ca /~roumani/fortran/labs/slatecIndex.htm (11408 words)

	The exponential integral, error function, and related integrals (Site not responding. Last check: 2007-10-08)
		The exponential integral, error function, and related integrals
		), and the cosine and sine integrals Ci(
		Note that, Maple V can do these examples, but the answer involves complex error functions and exponential integrals of complex arguments
	www.bl.physik.tu-muenchen.de /rechner/maple/summary-V2/subsection3_4_5.html (111 words)

	ExpIntegralRelated Members (Site not responding. Last check: 2007-10-08)
		This function program computes approximate values for the exponential integral E1(x), where x is real.
		This function program computes approximate values for the exponential integral Ei(x), where x is real.
		This function program computes approximate values for the function exp(-x) * Ei(x), where Ei(x) is the exponential integral, and x is real.
	altaxo.sourceforge.net /CoreClassRef/Altaxo.Calc.ExpIntegralRelatedMembers.html (130 words)

	On a family of logarithmic and exponential integrals occurring in probability and reliability theory (Site not responding. Last check: 2007-10-08)
		On a family of logarithmic and exponential integrals occurring in probability and reliability theory
		, x; a, b) satisfies a functional recurrence relation which is exploited to find a closed form evaluation of some incomplete integrals.
		New integral representations of the exponential integral and complimentary error functions are found as special cases.
	anziamj.austms.org.au /V35/part4/Chaudhry_2.html (111 words)

	The Mathematica Book Online: Advanced Mathematics in Mathematica \| Mathematical Functions
		Note that the Pochhammer symbol has a definite value even when the gamma functions which appear in its definition are infinite.
		The Lerch transcendent is related to integrals of the Fermi-Dirac distribution in statistical mechanics by
		The error function Erf[z] is the integral of the Gaussian distribution, given by
	documents.wolfram.com /mathematica/book/section-3.2.11 (2167 words)

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