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File:DiskLaserScalingLimit01.jpg ...represents the simplest rough estimate <math> \beta=s^{1/3}</math> without coefficients, which applies to both cases. Circles correspond to various experimental da(1,518 × 1,041 (56 KB)) - 09:39, 21 June 2013
File:DSC01693bangkokA.JPG .. In order to get $a_3$, we equalize coefficients with $\varepsilon^3$, and so on, getting the asymptotic series. The series(1,143 × 1,098 (109 KB)) - 09:43, 21 June 2013
File:Sqrt2figf45bT.png Value of $k$ and other coefficients are found substituting the expansion into the [[Transfer equation]] $F(z\!+(2,180 × 2,159 (1.01 MB)) - 08:52, 1 December 2018
File:SuZex0map48small.png Coefficients $c$ are calculated with [[Mathematica]], from the [[asymptotic expansion]](1,230 × 1,230 (734 KB)) - 09:43, 21 June 2013
File:SuZexoMapJPG.jpg Coefficients $a$ are calculated substituting the approximation (1) into the [[transfer e(4,576 × 4,542 (1.73 MB)) - 17:15, 25 September 2013
File:Aunem11mbp.jpg // Now coefficients are calcualted(3,569 × 3,536 (1.16 MB)) - 08:30, 1 December 2018
File:Ausintay40t50.jpg N=40; //720 points were used for Cauchi; last 3 coefficients are poor; last 4 digits are wrong.(2,274 × 2,871 (1.7 MB)) - 08:30, 1 December 2018
File:Hermiten.jpg DB HermitH0[7][7]= // COEFFICIENTS OF EVEN HERMITEH DB HermitH1[7][7]= // COEFFICIENTS OF ODD HERMITEH(1,257 × 1,473 (227 KB)) - 08:37, 1 December 2018
File:Hermiten6map.jpg DB HermiteH0[41][41]= // COEFFICIENTS OF EVEN normalized HERMITEH DB HermiteH1[41][41]= // COEFFICIENTS OF ODD normalized HERMITEH(1,307 × 880 (630 KB)) - 08:37, 1 December 2018
File:Koriasmap.jpg ...the asymptotic expansion of function [[besselJ0]]. Approximaitons of these coefficients can be extracted from the code below.(1,379 × 1,354 (941 KB)) - 08:40, 1 December 2018
File:Korifit76plot.jpg where $L_n=\mathrm{BesselJZero}[0,n]$ and coefficients $a$ and $b$ are:(3,831 × 863 (318 KB)) - 08:40, 1 December 2018
File:Koritestplot.jpg ...ted using the [[Mathematica]] routine [[Series]]; approximations for these coefficients can be extracted from the C++ code below.(1,618 × 996 (144 KB)) - 08:40, 1 December 2018
File:Norifit76fragment.jpg where $L_n=\mathrm{BesselJZero}[0,n]$ and coefficients $a$ and $b$ are:(967 × 448 (155 KB)) - 08:44, 1 December 2018
File:Norifit76plot.jpg where $L_n=\mathrm{BesselJZero}[0,n]$ and coefficients $a$ and $b$ are:(1,070 × 448 (168 KB)) - 08:44, 1 December 2018
File:Sunem0map6.jpg (* Coefficients of the asymptotic expansion of function SuNem can be computed with the Math (* The resulting array of coefficients should be stored in file [[sunema.txt]], it should be included at the compi(2,615 × 2,594 (1.15 MB)) - 08:53, 1 December 2018
File:Sunem0mdp.jpg (* Coefficients of the asymptotic expansion of function SuNem can be computed with the Math (* The resulting array of coefficients should be stored in file [[sunema.txt]], it should be included at the compi(2,158 × 2,141 (822 KB)) - 08:53, 1 December 2018
File:Sunem1map6.jpg (* Coefficients of the asymptotic expansion of function SuNem can be computed with the Math (* The resulting array of coefficients should be stored in file [[sunema.txt]],(2,615 × 2,594 (995 KB)) - 08:53, 1 December 2018
File:Sunem2map6.jpg (* Coefficients of the asymptotic expansion of function SuNem can be computed with the Math (* The resulting array of coefficients should be stored in file [[sunema.txt]],(2,615 × 2,594 (983 KB)) - 08:53, 1 December 2018
File:Susinmap8t.jpg Coefficients $A$ are determined with substitution of(4,312 × 4,283 (1.78 MB)) - 08:53, 1 December 2018
File:Tet2uMap.jpg fprintf(o,"z_type(%19.16lf,%19.16lf), 1.,\n", Re(L),Im(L)); // 0th and 1st coefficients are here! For [[tetration]] to arbitrary base, the coefficients of the expansion are calculated by [[Wiliam Paulsen]] and [[Samuel Cowgill](1,729 × 1,120 (526 KB)) - 07:21, 24 July 2020
