Rule: Q[1, 2, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-3\cdot t$
• $P_3$:
  $t^{73}-\frac{23293494351119190465563086097390638142347}{9080793633948628910411934536486610364}\cdot t^{71}+\frac{28232908817535069812045283229371371828266735}{9080793633948628910411934536486610364}\cdot t^{69}-\frac{1266087941575009091648907871205804285174696835}{534164331408742877083054972734506492}\cdot t^{67}+\frac{681796163362117098241898257586405451469203213615}{534164331408742877083054972734506492}\cdot t^{65}-\frac{69031270569939383791785719693835468768041646175110}{133541082852185719270763743183626623}\cdot t^{63}+\frac{21859193418896150838767763704871892824859644472701630}{133541082852185719270763743183626623}\cdot t^{61}-\frac{5555019447016709860507996348343231890752967371598723950}{133541082852185719270763743183626623}\cdot t^{59}+\frac{1153945706145177914693172081410325838042746461097599620650}{133541082852185719270763743183626623}\cdot t^{57}-\frac{198579928709245842746714836037190417433257825872095262418225}{133541082852185719270763743183626623}\cdot t^{55}+\frac{28590232601018900090244312711186033358659888977468104528015725}{133541082852185719270763743183626623}\cdot t^{53}-\frac{65452271864234964167967116276552866630955069194198329750913725}{2519643072682749420203089494030691}\cdot t^{51}+\frac{6728560720212228840302110948344628054232684631016632457647035625}{2519643072682749420203089494030691}\cdot t^{49}-\frac{588254880346384881507928751673175730616726027410464479846858296250}{2519643072682749420203089494030691}\cdot t^{47}+\frac{43844881758688880731070028235041091225286131830279310763721205241250}{2519643072682749420203089494030691}\cdot t^{45}-\frac{2789693485490276845353766247248681493410559747909226250871631091541250}{2519643072682749420203089494030691}\cdot t^{43}+\frac{151569948233818754306161893736196238890929251243942265386119335084717500}{2519643072682749420203089494030691}\cdot t^{41}-\frac{14055433848450542059434105413235519190347062365471907161848260254267303125}{5039286145365498840406178988061382}\cdot t^{39}+\frac{555289988516983835497917228879348212848990280895460230221494797639406340625}{5039286145365498840406178988061382}\cdot t^{37}-\frac{18646759730613366170511625302769136309111033962032091999928279950760136628125}{5039286145365498840406178988061382}\cdot t^{35}+\frac{530417036209323749006600494230502251692976577029214670232912279542418785690625}{5039286145365498840406178988061382}\cdot t^{33}-\frac{6362311628299312455823178848845542491530170092077395015025760612625095512731250}{2519643072682749420203089494030691}\cdot t^{31}+\frac{128012880380149326480901312221248892731070167320703748323941111099438929074156250}{2519643072682749420203089494030691}\cdot t^{29}-\frac{2145615183407826817628385586258577574647938057971858409431167317436532108956906250}{2519643072682749420203089494030691}\cdot t^{27}+\frac{29711049311321036010761940717988584805673410543133002753666803494553629356116843750}{2519643072682749420203089494030691}\cdot t^{25}-\frac{336509718783631257764504906843345670985448723861130915232833419659175719424867203125}{2519643072682749420203089494030691}\cdot t^{23}+\frac{3079660461359490426929470417035367924946637687106940259526203651464542127069694890625}{2519643072682749420203089494030691}\cdot t^{21}-\frac{22437508374745451192367053067577296639544719151660829213255989013533894664612355703125}{2519643072682749420203089494030691}\cdot t^{19}+\frac{127774266091243644284762017659085575376616636643420465920132049506455390939097551640625}{2519643072682749420203089494030691}\cdot t^{17}-\frac{555815413531812046727905591566524792388005315375943379635768976037463057970371932343750}{2519643072682749420203089494030691}\cdot t^{15}+\frac{1793447527156064510559245333871717206051571033760288423726836088639042575206036816718750}{2519643072682749420203089494030691}\cdot t^{13}-\frac{4130329236843915319049162760849245671681278392547498434220048366756878287297748576718750}{2519643072682749420203089494030691}\cdot t^{11}+\frac{6442069361026446056107341262284537224266047967495294680344998095140587008116355547265625}{2519643072682749420203089494030691}\cdot t^9-\frac{25244226965355982505886257582659345965075921590398151680905984261459444916100534087109375}{10078572290730997680812357976122764}\cdot t^7+\frac{13821462411978091692949869012849744154558554608365478713344402804525539698013797744921875}{10078572290730997680812357976122764}\cdot t^5-\frac{3443114939008694138630081375108708716330986218239423253852048077454524001906109502734375}{10078572290730997680812357976122764}\cdot t^3+\frac{244770051454351601844302395545505163327579736174059144371903184229907817031642113671875}{10078572290730997680812357976122764}\cdot t$

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.