Q4743 EXACT ZUDILIN RECURRENCE AUDIT
ZETA5|1.0369277551433699263313654864570341680570809195015...
RESIDUALS|all exactly zero for n=2..28
TABLE
n|q_n|p_n|p_n/q_n|error_vs_zeta5
0|-1|0|0.00000000000000000000000000000000000000000000000000|-1.03692775514336992633136548645703
1|42|87/2|1.03571428571428571428571428571428571428571428571428|-0.00121346942908421204565120074274
2|-17934|-1190161/64|1.03692793715846994535519125683060109289617486338797|0.00000018201510001902382577037356
3|14290980|38410106195/2592|1.03692775511542124585223565606063284085831641469300|-0.00000000002794868047912983039640
4|-15226085070|-873032613281675/55296|1.03692775514337405273951964019813483102998271850536|0.00000000000000412640815415374110
5|19191613019292|573129106723432091021/28800000|1.03692775514336992572993830710994126915471483020100|-0.00000000000000000060142717934709
6|-26992352388411564|-21764339220676847947083239/777600000|1.03692775514336992633145252492958026684144958543791|0.00000000000000000000008703847254
7|41008495771961165448|30874240683548193418311135052027/726062400000|1.03692775514336992633136547391328381790501617442995|-0.00000000000000000000000001254375
8|-65973231446368694478030|-544945891955455128670159122029373553/7965941760000|1.03692775514336992633136548645883711637954810816946|0.00000000000000000000000000000180
9|110928314902253220943591020|111327977637942885607420230409629748015943/967861923840000|1.03692775514336992633136548645703390938361465029303|-0.00000000000000000000000000000000
10|-193181295882061950220671597684|-2261901917600949798406345254843560845136124689/11291722444800000|1.03692775514336992633136548645703416809414572905259|0.00000000000000000000000000000000
11|346178586377728656792586975283928|6661104454334006589958779750759898577854302512656781/18556563178137600000|1.03692775514336992633136548645703416805707561358016|-0.00000000000000000000000000000000
12|-635237311445279015236695195928245036|-171123667143709404655818805932816754940296973055842144783/259791884493926400000|1.03692775514336992633136548645703416805708092026092|0.00000000000000000000000000000000
13|1189206868706004710931694557315832488600|792970426812649964549021260306163947149531211479970315031731921/643059387796022765568000|1.03692775514336992633136548645703416805708091950180|0.00000000000000000000000000000000
14|-2264652786843981998621373871949531662517400|-2179053902924122148102869678746913038568309930818236830825569373/927935624525285376000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
15|4376859446438598882340704514422738135870078480|148903913148104550301264780683633846890556167851224360081554255121751/32809152438572590080000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
16|-8568915209074259129879007024183440288458589000910|-2764047850849396591907825586293382761279110384655574475329630463627051151/311079371269429002240000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
17|16967689326300048322455730075960049868028943833406220|22253836404570961421424618841219939251208162179994218119142049348933994293708010351/1264834456350334193386782720000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
18|-33938878959557076160380541589248090983110046473679579300|-14716299397117725240482834494948722191557075248678667842095664666514828334733393040297/418169759038273753731956736000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
19|68498870570205964715175961083876120564879413153434250326200|85802378508070753864737651805690616462129213534092676494466293775716591929820144234195144697569/1208001342549062370565601732395008000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
20|-139374890413231860194428972515209605342370418218517870930008820|-26858830500435941147789204941618848626692419706781614656877069240849316364675788519296920295796087/185846360392163441625477189599232000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
21|285668386878433654286697247055579587387649837176351290233330542440|3147078758346090851448945163211612648993868768683187177044803831421925345028711239861202141339614768587/10624216935752010079589779338756096000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
22|-589419294801561564960947038668299715815050505655308748929023743676680|-3401286130545370494483791112853619909340007740442496470970549340439960591964281926899293942273932313606249/5565066013965338613118455844110336000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
23|1223538212637517603304711489871649247065189500900659123605203558117668400|504932154453828694112816355071041365890621494351751843613733587153681980175843722942052742963738254054382809489089/397985263150263438057496460478318359347200|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
24|-2553996285238940528869865718315889775253912143465934047439550661277166733100|-2390445253177511095348562975023092452805369695924989677194219431172427632095421325514133648411236231391983097843275387763/902630576824797477514401972364826038999449600|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
25|5358433818876787122679177476122761070213785182238694787904756007036159794956792|28846766296543906161988093061529810738528253608089489466819259679500794958834551478346835143098809715484274265872379297418011/5191714065909628569279725394690493440000000000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
26|-11295316115647719825387422148484454198656694579606550179864406537192327973875264264|-10741478549711456004414680999634954008070637251309322037058887097466891959627526801568597692788472278160483475534794369647440019383/917101019995683211385118550603267752960000000000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
27|23913829115527347661464391912556156037142055436924457694001582946141390462542526985328|8289194495088489808643406975963375494624760505047880554868139318509116262635129793879431250097193136999327833941036305664900671362745657/334283321788426530549875711694891095953920000000000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
28|-50833951953426853426866795134522643843109963545934828867390539159918794276553312853220760|-78687830763717202253343659245546162376615334523891168617244708356789833945943710711498121583591811765932085894168421846029238454707214741/1492812282308762815852714501986754495488000000000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
29|108465260330221924263009172946224598320981299104609946521084792542002936791351255222443761840|8482196277127968731606088332647716803315211328974771206415188597287321717109671715420275942020530562925707036751202446105474811350500478545848651/75416983131687433797080268977120979023089152000000000|1.03692775514336992633136548645703416805708091950191|0.00000000000000000000000000000000
MOBIUS
n|sigma1=q[n-1]/q[n]|sigma2=q[n-2]/q[n]|r=p[n]/q[n]|u=p[n-1]/q[n]|v=p[n-2]/q[n]
2|-0.0023419203747072599531615925058548009367|0.0000557600089216014274562283929965428794|1.0369279371584699453551912568306010928961|-0.0024255603880896620943459350953496152559|0.0000000000000000000000000000000000000000
3|-0.0012549174374325623575150199636414017793|0.0000029389167152987408841101170108697933|1.0369277551154212458522356560606328408583|-0.0013012589497011401597371208972372783392|0.0000030438780265594102013997640469722860
4|-0.0009385853247436243307420322983917230931|0.0000011778470905390784080257342211210961|1.0369277551433740527395196401981348310299|-0.0009732451737706850153602473413771214872|0.0000012213425538807921555898675929307677
5|-0.0007933718262604748609605101448403444924|0.0000007446471531931300991010049091831631|1.0369277551433699257299383071099412691547|-0.0008226692667982731768700372639035517075|0.0000007721453009136415772256041953437174
LIMITS
mu_dom|-2368.3175221384463
sigma1_star|-0.000422240679576217
sigma2_star|1.782871914889856e-7
r_star|1.03692775514337
u_star|-0.00043783308000317774
v_star|1.8487093724148996e-7