Rule: Q[21, 36]

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.

• $P_1$:
  $2097152\cdot t^{21}-220200960\cdot t^{19}+9413591040\cdot t^{17}-213374730240\cdot t^{15}+2800543334400\cdot t^{13}-21844238008320\cdot t^{11}+100119424204800\cdot t^9-257449947955200\cdot t^7+337903056691200\cdot t^5-187723920384000\cdot t^3+28158588057600\cdot t$
• $P_2$:
  $2097152\cdot t^{57}-\frac{431266610190358621801010908102656}{343303287907604831431525}\cdot t^{55}+\frac{119695523318938213881198733280673792}{343303287907604831431525}\cdot t^{53}-\frac{94157758587981571422999389646922973184}{1579195124374982224585015}\cdot t^{51}+\frac{122426406211768399968828016372527804383232}{17371146368124804470435165}\cdot t^{49}-\frac{2127297709596759005491257909683448246435840}{3474229273624960894087033}\cdot t^{47}+\frac{705166860466398181330847361078586827116937216}{17371146368124804470435165}\cdot t^{45}-\frac{36559564362032251686797569471487052856978931712}{17371146368124804470435165}\cdot t^{43}+\frac{301416769071551832633596627755885962628472438784}{3474229273624960894087033}\cdot t^{41}-\frac{9991970169011998867424708242917801979135606161408}{3474229273624960894087033}\cdot t^{39}+\frac{268382885310822384765442243093486547561600789369856}{3474229273624960894087033}\cdot t^{37}-\frac{5867947571248962690977655290122416379966945461912576}{3474229273624960894087033}\cdot t^{35}+\frac{104669341206599698627812115697988389377952696250239232}{3474229273624960894087033}\cdot t^{33}-\frac{138496422208591976104438874952644779415013843799418880}{315839024874996444917003}\cdot t^{31}+\frac{1642018188674324804213902335265586271549232047597384960}{315839024874996444917003}\cdot t^{29}-\frac{15801029888617261339523148975996104757449147974332476160}{315839024874996444917003}\cdot t^{27}+\frac{122734042996850449768097612488091254938383457606970533600}{315839024874996444917003}\cdot t^{25}-\frac{33203372638496982935419732111030376748660720475584676800}{13732131516304193257261}\cdot t^{23}+\frac{163848945533061250632214607623974805426902899657242708500}{13732131516304193257261}\cdot t^{21}-\frac{633032626364006323771606117357922774871781326106951924500}{13732131516304193257261}\cdot t^{19}+\frac{1883554064605383073125954233400323381683561353087006199125}{13732131516304193257261}\cdot t^{17}-\frac{4225935961086012916046843408472497994692689332411412555500}{13732131516304193257261}\cdot t^{15}+\frac{13911046884005759060345008389438453321085391957338317647625}{27464263032608386514522}\cdot t^{13}-\frac{16194514034912312179016122792061167994098073571257210596875}{27464263032608386514522}\cdot t^{11}+\frac{25363922436958705080585678234558530636767013032373218753125}{54928526065216773029044}\cdot t^9-\frac{3107600435397868832710666745003711675122961586633086225625}{13732131516304193257261}\cdot t^7+\frac{54584908442380668654488506443791846519411910125964612309375}{878856417043468368464704}\cdot t^5-\frac{6931255637463360129590431469199120113045897370906599596875}{878856417043468368464704}\cdot t^3+\frac{1067583015073643668378398532684940793829042330432387321875}{3515425668173873473858816}\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.