Rule: Q[3, 70]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{73}-\frac{23293494351119190465563086097390638142347}{2270198408487157227602983634121652591}\cdot t^{71}+\frac{28232908817535069812045283229371371828266735}{4540396816974314455205967268243305182}\cdot t^{69}-\frac{1266087941575009091648907871205804285174696835}{534164331408742877083054972734506492}\cdot t^{67}+\frac{681796163362117098241898257586405451469203213615}{1068328662817485754166109945469012984}\cdot t^{65}-\frac{34515635284969691895892859846917734384020823087555}{267082165704371438541527486367253246}\cdot t^{63}+\frac{10929596709448075419383881852435946412429822236350815}{534164331408742877083054972734506492}\cdot t^{61}-\frac{2777509723508354930253998174171615945376483685799361975}{1068328662817485754166109945469012984}\cdot t^{59}+\frac{576972853072588957346586040705162919021373230548799810325}{2136657325634971508332219890938025968}\cdot t^{57}-\frac{198579928709245842746714836037190417433257825872095262418225}{8546629302539886033328879563752103872}\cdot t^{55}+\frac{28590232601018900090244312711186033358659888977468104528015725}{17093258605079772066657759127504207744}\cdot t^{53}-\frac{65452271864234964167967116276552866630955069194198329750913725}{645028626606783851571990910471856896}\cdot t^{51}+\frac{6728560720212228840302110948344628054232684631016632457647035625}{1290057253213567703143981820943713792}\cdot t^{49}-\frac{294127440173192440753964375836587865308363013705232239923429148125}{1290057253213567703143981820943713792}\cdot t^{47}+\frac{21922440879344440365535014117520545612643065915139655381860602620625}{2580114506427135406287963641887427584}\cdot t^{45}-\frac{1394846742745138422676883123624340746705279873954613125435815545770625}{5160229012854270812575927283774855168}\cdot t^{43}+\frac{37892487058454688576540473434049059722732312810985566346529833771179375}{5160229012854270812575927283774855168}\cdot t^{41}-\frac{14055433848450542059434105413235519190347062365471907161848260254267303125}{82563664205668333001214836540397682688}\cdot t^{39}+\frac{555289988516983835497917228879348212848990280895460230221494797639406340625}{165127328411336666002429673080795365376}\cdot t^{37}-\frac{18646759730613366170511625302769136309111033962032091999928279950760136628125}{330254656822673332004859346161590730752}\cdot t^{35}+\frac{530417036209323749006600494230502251692976577029214670232912279542418785690625}{660509313645346664009718692323181461504}\cdot t^{33}-\frac{3181155814149656227911589424422771245765085046038697507512880306312547756365625}{330254656822673332004859346161590730752}\cdot t^{31}+\frac{64006440190074663240450656110624446365535083660351874161970555549719464537078125}{660509313645346664009718692323181461504}\cdot t^{29}-\frac{1072807591703913408814192793129288787323969028985929204715583658718266054478453125}{1321018627290693328019437384646362923008}\cdot t^{27}+\frac{14855524655660518005380970358994292402836705271566501376833401747276814678058421875}{2642037254581386656038874769292725846016}\cdot t^{25}-\frac{336509718783631257764504906843345670985448723861130915232833419659175719424867203125}{10568149018325546624155499077170903384064}\cdot t^{23}+\frac{3079660461359490426929470417035367924946637687106940259526203651464542127069694890625}{21136298036651093248310998154341806768128}\cdot t^{21}-\frac{22437508374745451192367053067577296639544719151660829213255989013533894664612355703125}{42272596073302186496621996308683613536256}\cdot t^{19}+\frac{127774266091243644284762017659085575376616636643420465920132049506455390939097551640625}{84545192146604372993243992617367227072512}\cdot t^{17}-\frac{277907706765906023363952795783262396194002657687971689817884488018731528985185966171875}{84545192146604372993243992617367227072512}\cdot t^{15}+\frac{896723763578032255279622666935858603025785516880144211863418044319521287603018408359375}{169090384293208745986487985234734454145024}\cdot t^{13}-\frac{2065164618421957659524581380424622835840639196273749217110024183378439143648874288359375}{338180768586417491972975970469468908290048}\cdot t^{11}+\frac{6442069361026446056107341262284537224266047967495294680344998095140587008116355547265625}{1352723074345669967891903881877875633160192}\cdot t^9-\frac{25244226965355982505886257582659345965075921590398151680905984261459444916100534087109375}{10821784594765359743135231055023005065281536}\cdot t^7+\frac{13821462411978091692949869012849744154558554608365478713344402804525539698013797744921875}{21643569189530719486270462110046010130563072}\cdot t^5-\frac{3443114939008694138630081375108708716330986218239423253852048077454524001906109502734375}{43287138379061438972540924220092020261126144}\cdot t^3+\frac{244770051454351601844302395545505163327579736174059144371903184229907817031642113671875}{86574276758122877945081848440184040522252288}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.