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 superfunctions of eta converge towards each other sheldonison Long Time Fellow Posts: 641 Threads: 22 Joined: Oct 2008 05/30/2011, 06:06 AM (This post was last modified: 05/30/2011, 07:28 AM by sheldonison.) (05/24/2011, 02:18 PM)sheldonison Wrote: ..... I originally thought I would calculate theta(z) by generating a Kneser Riemann mapping, which would require some modifications to my Kneser.gp code, that I haven't had time to try yet. So yesterday I calculated $\theta(z)$, the easier way, using the equation. $\theta(z)=\text{cheta}^{[-1]}(\text{sexp}_\eta(z))-z$..... This time, I calculated the Kneser Riemann mapping from cheta(z), which is the upper super-exponential of eta, calculating $\text{sexp}_\eta(z)$, and theta(z) using my iterated Kneser/Riemann mapping algorithm $\text{sexp}_\eta(z) = \text{cheta(z+\theta(z))$ Here are the first 80 terms of the resulting $\text{sexp}_\eta$taylor series, centered at 0, accurate to nearly 50 decimal digits, which is comparable to the accuracy of the cheta series from which it was generated. This required approximately 20 iterations of the iterative Kneser mapping algorithm. Code:a0=   1 a1=   0.611095453771651725262810441596468781580269047357550 a2=  -0.231702614476767880057754637266321761121523435531760 a3=   0.0917812876620532822133071038897611328881116958928124 a4=  -0.0375649217050071576220508834372714135192894502813784 a5=   0.0157737222017623151244855920986092095582090932573677 a6=  -0.00676146377741411160378256866430459401065680422398120 a7=   0.00294774761901529095651004530936485553141374655276524 a8=  -0.00130329397044496937265810128322368856058033652210951 a9=   0.000583068821879779779750519504424021334792203212824801 a10= -0.000263475538289731186662273991418485660413024460182638 a11=  0.000120079821309960737865224745056228269329158138384658 a12= -0.0000551303455271971740777327708851583454767974089869403 a13=  0.0000254727117285946134566265036623587110503043495453153 a14= -0.0000118350189839471092554362143395131603304332488176578 a15=  0.00000552555661721659732404978764658822685255716631441388 a16= -0.00000259088250250205448643621195471018577614859681535859 a17=  0.00000121947772793691463866748710287359617069950224343485 a18= -0.000000575938244261633170948573966605515258622439917077526 a19=  0.000000272835731915044808130761045812419754647293505221581 a20= -0.000000129604098503712840293865769356787634917932600346819 a21=  0.0000000617184648746551109652382067118582400221072683266451 a22= -0.0000000294572386417802551977422981166350346746812044161570 a23=  0.0000000140884643093386428902074176969660501764922998188352 a24= -0.00000000675079178733813416073761444717751772347711978606630 a25=  0.00000000324040197028192052818961738454119586307326826755909 a26= -0.00000000155789250617035227640871356618398318683270179424542 a27=  0.000000000750098596635507780777134988279191034195969015855036 a28= -0.000000000361655381928347049065842422084443198416688544391361 a29=  1.74592476875241231046123466193763330740029059024297 E-10 a30= -8.43864351753681771955715994960529383687218538708627 E-11 a31=  4.08321688631192290465015221458217806927196611211009 E-11 a32= -1.97780890956079928000397935766378593927042952963150 E-11 a33=  9.58937887210731107030786818689412786447899880426182 E-12 a34= -4.65366990984925474622297498839447451648951394617092 E-12 a35=  2.26035419763439608928450172822433746171836295149080 E-12 a36= -1.09878336817672683270058936312912776149186915209576 E-12 a37=  5.34543285201212110206484945017316458298407068619223 E-13 a38= -2.60238186381938710165111994894080921153824458691605 E-13 a39=  1.26782708786448072052855802829491283561033763740595 E-13 a40= -6.18065713730427984232303419660068094462142609552625 E-14 a41=  3.01495472825825957301602049941641113658174693814225 E-14 a42= -1.47158505471116819772042780418571488834513678652714 E-14 a43=  7.18681076071295928780918874220139590820603352332199 E-15 a44= -3.51173708545661500664450320814947737493335672976064 E-15 a45=  1.71684924476025713957768891113604892326056846887684 E-15 a46= -8.39763218512702291011716365584708191307710741717839 E-16 a47=  4.10947958309355559866994137817039774676100895009521 E-16 a48= -2.01193271357506415016943567634048365900544091276272 E-16 a49=  9.85436431469814660806778049713979975055654894405037 E-17 a50= -4.82863851527806912924306619834010899289430282129108 E-17 a51=  2.36697966470193428295397824205341791955432902543780 E-17 a52= -1.16073041261193125343825164385537017757777134584090 E-17 a53=  5.69414919431601466980627541017375839178407746579289 E-18 a54= -2.79435099362766606225911963240953587959485181378627 E-18 a55=  1.37177230600201211382050307050494974722622608593200 E-18 a56= -6.73638185995954869619382195705443352315783218342629 E-19 a57=  3.30909986107458123646909880258274197989614291968962 E-19 a58= -1.62602320761063609954141455195401222493393280029547 E-19 a59=  7.99231746118155302579947571730532923235669071272187 E-20 a60= -3.92955608509546808441160057820325985041095375019077 E-20 a61=  1.93256856644514224462909823307272388335074142227301 E-20 a62= -9.50699052849564802556568302196070479320577453210153 E-21 a63=  4.67804295847118247466699947260215068151288567726025 E-21 a64= -2.30247426862419264122607788485950688773998006169473 E-21 a65=  1.13352579378475997563046656633740111440713354501555 E-21 a66= -5.58175580272975796962068914975815305014506076078419 E-22 a67=  2.74922300731523716070763631069703995807246909834284 E-22 a68= -1.35439662860401999858849559830664314463541594037131 E-22 a69=  6.67383845978854646769324758362458777997658711938811 E-23 a70= -3.28924895518170155123068794530223425760681766093393 E-23 a71=  1.62146075255442663131012653517379778869865486264882 E-23 a72= -7.99470232162273878609029211157712241122041145401289 E-24 a73=  3.94259292573183323472088911673635062652752328594458 E-24 a74= -1.94465732147586014876037988016159230543477617405982 E-24 a75=  9.59364278594765374296940813010099907533150668148673 E-25 a76= -4.73370532201367019577101005937731419703884318213035 E-25 a77=  2.33611431476000136896220802065677131157325649743031 E-25 a78= -1.15308206561872134295524237335114322979399731394009 E-25 a79=  5.69243045052281048821530522001513494796180617476246 E-26 a80= -2.81063753494564060709822549726337867231556147101730 E-26 « Next Oldest | Next Newest »

 Messages In This Thread superfunctions of eta converge towards each other - by sheldonison - 05/23/2011, 09:01 PM RE: superfunctions of eta converge towards each other - by bo198214 - 05/23/2011, 09:49 PM RE: superfunctions of eta converge towards each other - by sheldonison - 05/23/2011, 11:26 PM RE: superfunctions of eta converge towards each other - by bo198214 - 05/24/2011, 01:06 PM RE: superfunctions of eta converge towards each other - by sheldonison - 05/24/2011, 02:18 PM RE: superfunctions of eta converge towards each other - by bo198214 - 05/24/2011, 02:27 PM RE: superfunctions of eta converge towards each other - by sheldonison - 05/30/2011, 06:06 AM RE: superfunctions of eta converge towards each other - by sheldonison - 05/25/2011, 04:03 AM RE: superfunctions of eta converge towards each other - by sheldonison - 05/27/2011, 09:36 AM RE: superfunctions of eta converge towards each other - by tommy1729 - 05/25/2011, 11:04 PM RE: superfunctions of eta converge towards each other - by bo198214 - 05/25/2011, 11:15 PM RE: superfunctions of eta converge towards each other - by tommy1729 - 05/26/2011, 12:10 PM RE: superfunctions of eta converge towards each other - by tommy1729 - 06/06/2011, 10:42 PM

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