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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-3\cdot t$
• $P_3$:
  $t^9-\frac{117}{4}\cdot t^7+\frac{945}{4}\cdot t^5-\frac{2205}{4}\cdot t^3+\frac{945}{4}\cdot t$
• $P_4$:
  $t^{19}-\frac{23713751}{205892}\cdot t^{17}+\frac{2134183615}{411784}\cdot t^{15}-\frac{48885080515}{411784}\cdot t^{13}+\frac{623352876985}{411784}\cdot t^{11}-\frac{4536269518165}{411784}\cdot t^9+\frac{18427952550645}{411784}\cdot t^7-\frac{38805894891225}{411784}\cdot t^5+\frac{36681698574675}{411784}\cdot t^3-\frac{11110847880825}{411784}\cdot t$
• $P_5$:
  $t^{41}-\frac{20186539540935324640978282625139084335195484869011510131338502173541414255442317992772533506348506636102216085049401123}{35568538848339947881892718663924101777326132051654956865080221854355911613679822055724775480400251645497948138311656}\cdot t^{39}+\frac{61457071084921257944284584872696717826580934225725094864849136586358864585974318600885044373988102516723884506285205669445}{426822466180079374582712623967089221327913584619859482380962662252270939364157864668697305764803019745975377659739872}\cdot t^{37}-\frac{18487552757429280625816423834062605802076016180584700259163439391457622438551328341373269747102369196181135660146048657766745}{853644932360158749165425247934178442655827169239718964761925324504541878728315729337394611529606039491950755319479744}\cdot t^{35}+\frac{167798323492690130816951591743965070837969602064556627223831116317059006336700007047476504027751426916621111802267674577979359115}{77681688844774446174053697562010238281680272400814425793335204529913310964276731369702909649194149593767518734072656704}\cdot t^{33}-\frac{11763693076467864608998679296514406421219184392774871603681437457182530766148281397003884748285240400542198967384343505186654694265}{77681688844774446174053697562010238281680272400814425793335204529913310964276731369702909649194149593767518734072656704}\cdot t^{31}+\frac{599701890586492249692535509787331610459558790209026555904578641996068174967574154262346903234608306991742752799447699908137881321145}{77681688844774446174053697562010238281680272400814425793335204529913310964276731369702909649194149593767518734072656704}\cdot t^{29}-\frac{22693876053375036804967850909729346781486029321940125904089475051166266613832166924107905525598829181482011273835513145557222240823575}{77681688844774446174053697562010238281680272400814425793335204529913310964276731369702909649194149593767518734072656704}\cdot t^{27}+\frac{71697600618933697626660896379140027088453895188450537791352932285374362319256872595850889809119705296796363656570290476779500411136275}{8631298760530494019339299729112248697964474711201602865926133836657034551586303485522545516577127732640835414896961856}\cdot t^{25}-\frac{220182475063239394219325463029839739000555898122769857666425036426845996407436225769577416026080386513228060195675064475921741176878875}{1233042680075784859905614247016035528280639244457371837989447690951004935940900497931792216653875390377262202128137408}\cdot t^{23}+\frac{25081710485328395120529642174508576691168490077431470094384903180604316943219219874128944521896378882037913223536069960014381101682510625}{8631298760530494019339299729112248697964474711201602865926133836657034551586303485522545516577127732640835414896961856}\cdot t^{21}-\frac{43999159754913915487886307126286776516169800342106311230379180921411236896397177506418365381392996747625368944389049960715146260812744375}{1233042680075784859905614247016035528280639244457371837989447690951004935940900497931792216653875390377262202128137408}\cdot t^{19}+\frac{404452642781559611691738853356016815346504172698534865671314545641260047270282385140080571977012353045014757997583902956220673037187336875}{1233042680075784859905614247016035528280639244457371837989447690951004935940900497931792216653875390377262202128137408}\cdot t^{17}-\frac{2745029705461398886433219965935493642500582284294554267410933754783005276631343977351373625092613446393150718221561660531585687853099253125}{1233042680075784859905614247016035528280639244457371837989447690951004935940900497931792216653875390377262202128137408}\cdot t^{15}+\frac{1035614304144575148167224169247816186386991481060479229770600294330102073514309589231229270386734900196990555623277694754430543522516965625}{94849436928906527685047249770464271406203018804413218306880591611615764303146192148599401281067337721327861702164416}\cdot t^{13}-\frac{3552099288309566580729636197736803072171467482349013342317115338309517957646787788334861695321460530673408206262965457164036923371122189375}{94849436928906527685047249770464271406203018804413218306880591611615764303146192148599401281067337721327861702164416}\cdot t^{11}+\frac{8101876581853806660258038286023112882171865959664665798986874285638751269443555905420313498663487350108451519638495105479127531249472911875}{94849436928906527685047249770464271406203018804413218306880591611615764303146192148599401281067337721327861702164416}\cdot t^9-\frac{11337722413269233446562257779943935413427430703928736165666265206813755759397534595182427126925938458959168443262465113893739518655116603125}{94849436928906527685047249770464271406203018804413218306880591611615764303146192148599401281067337721327861702164416}\cdot t^7+\frac{8476031761029077938691521051001017422352381274279059999395025259644244667897860109167065937479156241944124335162150643909265223463120784375}{94849436928906527685047249770464271406203018804413218306880591611615764303146192148599401281067337721327861702164416}\cdot t^5-\frac{161102343691748229530571037999598820120692789976317882154864645712345227371100242822308239052147072512398159160975502793653234930557103125}{5928089808056657980315453110654016962887688675275826144180036975725985268946637009287462580066708607582991356385276}\cdot t^3+\frac{38026167010563526543677975214044988387315392887450023149815680688205957366806520148838216411108332424150121600144024875656568536155328125}{23712359232226631921261812442616067851550754701103304576720147902903941075786548037149850320266834430331965425541104}\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 (probabilists') type can be downloaded here packed into a single file.