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File:DoyaplotTc.png fprintf(o,"4 4 translate\n 100 100 scale\n"); for(n=0;n<4;n++){ M(0,n)L(2,n)}(881 × 1,325 (95 KB)) - 09:43, 21 June 2013File:Dzhioyeva0008py3y.jpeg (200 × 253 (8 KB)) - 09:39, 21 June 2013File:E1efig09abc1a150.png DO(m,M1) X[m]=-4.+.1*(m-.5); DO(n,N1) Y[n]=-4.+.05*(n-.5);(2,234 × 711 (883 KB)) - 08:34, 1 December 2018File:Edro2.jpg December 4, 2011(600 × 696 (98 KB)) - 09:40, 21 June 2013File:EkimovSide2.jpg Jul 4, 2012 by svpressa(497 × 533 (41 KB)) - 09:42, 21 June 2013File:EkimovUdaril.jpg (726 × 736 (90 KB)) - 09:42, 21 June 2013File:Elutin1a4tori.jpg </ref>. Namely for $u\!=\!4$, the iterates can be expressed through the elementary function,(922 × 914 (62 KB)) - 09:38, 21 June 2013File:Eps32x22ringRoster.jpg 32 22 4 [32 0 0 -22 0 22] fprintf(o,"%2d %2d 4 [%2d 0 0 %2d 0 %2d]\n<", M,N,M,-N,N);(322 × 222 (13 KB)) - 09:39, 21 June 2013File:Esqrt2iterMapT.png at the [[fixed point]] $L\!=\!4$, and the [[Abel function]] $G=F^{-1}$, the functions $F$ and $G$ are called $F_{4,5}$ and $F_{4,5}^{~-1}$.(1,092 × 1,080 (1.36 MB)) - 09:43, 21 June 2013File:ExpIte4T.jpg for(n=-4;n<5;n++) {M(-4,n)L(4,n)} for(m=-4;m<5;m++) {M(m,-4)L(m,4)}(1,673 × 1,673 (901 KB)) - 08:35, 1 December 2018File:ExpMapT.png DO(m,M1) X[m]=-4.+.02*(m-.5); DO(n,N1) Y[n]=-4.+.02*(n-.5);(1,742 × 1,726 (1.62 MB)) - 08:35, 1 December 2018File:ExpQ2mapT.png Note that lines $u\!=\!1$, $u\!=\!2$, $u\!=\!4$, $u\!=\!8$ passthrough the integer values at the real axis. DO(m,M1) X[m]=4.3* sinh( log(4.)*(-1.+.02*m) );(1,765 × 1,729 (1.15 MB)) - 08:35, 1 December 2018File:ExpQ2plotT.png The [[fixed point]]s $L\!=\!2$ and $L\!=\!4$ are solutions of the equation \put(590,792){\sx{4.2}{$y$}}(2,512 × 1,744 (175 KB)) - 08:35, 1 December 2018File:FacIteT.jpg %\put(11,976){\sx{4}{$y\!=\!\mathrm{pow}_2^c(x)$}} % <br> \put(13,991){\sx{4.4}{$y$}}% \!=\!\mathrm{Factorial}^n(x)$}} % <br>(2,093 × 2,093 (795 KB)) - 08:35, 1 December 2018File:FacmapT500.png 4.02688719234390123, 5.00276808075403005, 6.28391137081578218, 7.49591912 y=Im(z); if(fabs(y)>1.4)return expaun(z/2.)+expaun(z/2.-.5)+z*log(2.)-log(sqrt(M_PI));(2,355 × 2,334 (1.73 MB)) - 09:41, 21 June 2013File:Fafo2test0.png The step of the grid is $\sqrt{\pi/16}=\sqrt{\pi} /4 \approx 0.443$ fprintf(o,"%2d %2d 4 [%2d 0 0 %2d 0 %2d]\n<", M,N,M,-N,N);(642 × 642 (5 KB)) - 09:39, 21 June 2013File:Fafo2test1.png fprintf(o,"%2d %2d 4 [%2d 0 0 %2d 0 %2d]\n<", M,N,M,-N,N); 64 64 4 [64 0 0 -64 0 64](642 × 642 (8 KB)) - 09:39, 21 June 2013File:Fafo2test2.png fprintf(o,"%2d %2d 4 [%2d 0 0 %2d 0 %2d]\n<", M,N,M,-N,N); 64 64 4 [64 0 0 -64 0 64](642 × 642 (6 KB)) - 09:39, 21 June 2013File:Fafo2test3.png fprintf(o,"%2d %2d 4 [%2d 0 0 %2d 0 %2d]\n<", M,N,M,-N,N); 64 64 4 [64 0 0 -64 0 64](642 × 642 (8 KB)) - 09:39, 21 June 2013File:FFTexample16T.png for(m=-3;m<4;m++) {M(-5,m) L(5,m)} fprintf(o,".004 W S\n"); DO(j,N){x=X[j];y=Re(a[j]); if(j==0)M(x,y)else L(x,y);} fprintf(o,".04 W 0 .4 1 RGB S\n");(2,101 × 1,536 (155 KB)) - 09:39, 21 June 2013