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superfunctions of eta converge towards each other
#12
(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 , the easier way, using the equation.
.....

This time, I calculated the Kneser Riemann mapping from cheta(z), which is the upper super-exponential of eta, calculating , and theta(z) using my iterated Kneser/Riemann mapping algorithm
Here are the first 80 terms of the resulting 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
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Messages In This Thread
RE: superfunctions of eta converge towards each other - by sheldonison - 05/30/2011, 06:06 AM

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