C.S. Liu, "Exponential function rational expansion method for nonlinear differential- difference equations", in Chaos, Solitons and Fractals, vol. 40, 2009, pp. 708-716C. Liu, Exponential function rational expansion method for nonlinear differential- difference equations, Chaos, Solitons and ...
Ifs=1and we writetBin place ofB, then we get the expansion ofeA+tB. Corollary 1∂∂teA+tB|t=0=∫01euABe(1−u)Adu. Another important formula for the exponential function is theBaker-Campbell-Hausdorff formula. Theorem 2 (Baker-Campbell-Hausdorff formula) ...
Related to Exponential Function:exponential equation exponential function [‚ek·spə′nen·chəl ′fəŋk·shən] (mathematics) The function ƒ(x) =ex, written ƒ(x) = exp (x). McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hi...
afterall), we have a pretty good grasp on the exponential function. Positive integer exponents are just a shorthand for repeated multiplication. Negative integer exponents are just repeated division. Exponents of the form 1/n are just an alternative way of writing the nth root. By combining thes...
By setting up the linear recursion for five expansion coefficients and solving the matrix exponential function exp(i|v→|M5) one arrives at the following quasi-analytical formula for an SU(5) matrix U=exp(iλ→⋅v→)=∑j=15exp(izj|v→|)5zj4−3zj2−2ζzj−ξ{(zj...
Wolfram Research (1988), Exp, Wolfram Language function, https://reference.wolfram.com/language/ref/Exp.html (updated 2021).Give FeedbackTop Introduction for Programmers Introductory Book Wolfram Function Repository | Wolfram Data Repository | Wolfram Data Drop | Wolfram Language Products ©...
The Exponential Function 1 Theorem 1Let Tm,n=[∑k=0m1k!(An)n]mm,n∈N. Then limm→∞Tm,n=limn→∞Tm,n=eA. ProofThe matricesB=eA/nand T=∑k=0m1k!(An)k commute. Hence eA−Tm,n(A)=Bn−Tn=(B−T)(Bn−1+Bn−2T+⋯+Tn−1)....
Ramanujan’s approximation to the exponential function is reexamined with the help of Perron’s saddle-point method. This allows for a wide generalization that includes the results of Buckholtz, and where all the asymptotic expansion coefficients may be given in closed form. Ramanujan’s approximation...
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x = expinv(p,mu) [x,xLo,xUp] = expinv(p,mu,pCov) [x,xLo,xUp] = expinv(p,mu,pCov,alpha) Description x= expinv(p)returns the inverse cumulative distribution function (icdf) of the standard exponential distribution, evaluated at the values inp. ...