Rule: Q[1, 2, 6, 10, 22]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-3\cdot t$
• $P_3$:
  $2\cdot t^9-\frac{117}{4}\cdot t^7+\frac{945}{8}\cdot t^5-\frac{2205}{16}\cdot t^3+\frac{945}{32}\cdot t$
• $P_4$:
  $2\cdot t^{19}-\frac{23713751}{205892}\cdot t^{17}+\frac{2134183615}{823568}\cdot t^{15}-\frac{48885080515}{1647136}\cdot t^{13}+\frac{623352876985}{3294272}\cdot t^{11}-\frac{4536269518165}{6588544}\cdot t^9+\frac{18427952550645}{13177088}\cdot t^7-\frac{38805894891225}{26354176}\cdot t^5+\frac{36681698574675}{52708352}\cdot t^3-\frac{11110847880825}{105416704}\cdot t$
• $P_5$:
  $2\cdot t^{41}-\frac{20186539540935324640978282625139084335195484869011510131338502173541414255442317992772533506348506636102216085049401123}{35568538848339947881892718663924101777326132051654956865080221854355911613679822055724775480400251645497948138311656}\cdot t^{39}+\frac{61457071084921257944284584872696717826580934225725094864849136586358864585974318600885044373988102516723884506285205669445}{853644932360158749165425247934178442655827169239718964761925324504541878728315729337394611529606039491950755319479744}\cdot t^{37}-\frac{18487552757429280625816423834062605802076016180584700259163439391457622438551328341373269747102369196181135660146048657766745}{3414579729440634996661700991736713770623308676958875859047701298018167514913262917349578446118424157967803021277918976}\cdot t^{35}+\frac{167798323492690130816951591743965070837969602064556627223831116317059006336700007047476504027751426916621111802267674577979359115}{621453510758195569392429580496081906253442179206515406346681636239306487714213850957623277193553196750140149872581253632}\cdot t^{33}-\frac{11763693076467864608998679296514406421219184392774871603681437457182530766148281397003884748285240400542198967384343505186654694265}{1242907021516391138784859160992163812506884358413030812693363272478612975428427701915246554387106393500280299745162507264}\cdot t^{31}+\frac{599701890586492249692535509787331610459558790209026555904578641996068174967574154262346903234608306991742752799447699908137881321145}{2485814043032782277569718321984327625013768716826061625386726544957225950856855403830493108774212787000560599490325014528}\cdot t^{29}-\frac{22693876053375036804967850909729346781486029321940125904089475051166266613832166924107905525598829181482011273835513145557222240823575}{4971628086065564555139436643968655250027537433652123250773453089914451901713710807660986217548425574001121198980650029056}\cdot t^{27}+\frac{71697600618933697626660896379140027088453895188450537791352932285374362319256872595850889809119705296796363656570290476779500411136275}{1104806241347903234475430365326367833339452763033805166838545131092100422603046846146885826121872349778026933106811117568}\cdot t^{25}-\frac{220182475063239394219325463029839739000555898122769857666425036426845996407436225769577416026080386513228060195675064475921741176878875}{315658926099400924135837247236105095239843646581087190525298608883457263600870527470538807463392099936579123744803176448}\cdot t^{23}+\frac{25081710485328395120529642174508576691168490077431470094384903180604316943219219874128944521896378882037913223536069960014381101682510625}{4419224965391612937901721461305471333357811052135220667354180524368401690412187384587543304487489399112107732427244470272}\cdot t^{21}-\frac{43999159754913915487886307126286776516169800342106311230379180921411236896397177506418365381392996747625368944389049960715146260812744375}{1262635704397603696543348988944420380959374586324348762101194435533829054403482109882155229853568399746316494979212705792}\cdot t^{19}+\frac{404452642781559611691738853356016815346504172698534865671314545641260047270282385140080571977012353045014757997583902956220673037187336875}{2525271408795207393086697977888840761918749172648697524202388871067658108806964219764310459707136799492632989958425411584}\cdot t^{17}-\frac{2745029705461398886433219965935493642500582284294554267410933754783005276631343977351373625092613446393150718221561660531585687853099253125}{5050542817590414786173395955777681523837498345297395048404777742135316217613928439528620919414273598985265979916850823168}\cdot t^{15}+\frac{1035614304144575148167224169247816186386991481060479229770600294330102073514309589231229270386734900196990555623277694754430543522516965625}{777006587321602274795907070119643311359615130045753084369965806482356341171373606081326295294503630613117843064130895872}\cdot t^{13}-\frac{3552099288309566580729636197736803072171467482349013342317115338309517957646787788334861695321460530673408206262965457164036923371122189375}{1554013174643204549591814140239286622719230260091506168739931612964712682342747212162652590589007261226235686128261791744}\cdot t^{11}+\frac{8101876581853806660258038286023112882171865959664665798986874285638751269443555905420313498663487350108451519638495105479127531249472911875}{3108026349286409099183628280478573245438460520183012337479863225929425364685494424325305181178014522452471372256523583488}\cdot t^9-\frac{11337722413269233446562257779943935413427430703928736165666265206813755759397534595182427126925938458959168443262465113893739518655116603125}{6216052698572818198367256560957146490876921040366024674959726451858850729370988848650610362356029044904942744513047166976}\cdot t^7+\frac{8476031761029077938691521051001017422352381274279059999395025259644244667897860109167065937479156241944124335162150643909265223463120784375}{12432105397145636396734513121914292981753842080732049349919452903717701458741977697301220724712058089809885489026094333952}\cdot t^5-\frac{161102343691748229530571037999598820120692789976317882154864645712345227371100242822308239052147072512398159160975502793653234930557103125}{1554013174643204549591814140239286622719230260091506168739931612964712682342747212162652590589007261226235686128261791744}\cdot t^3+\frac{38026167010563526543677975214044988387315392887450023149815680688205957366806520148838216411108332424150121600144024875656568536155328125}{12432105397145636396734513121914292981753842080732049349919452903717701458741977697301220724712058089809885489026094333952}\cdot t$

Warning: This rule has negative weights!

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.