Rule: Q[11, 20]

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.

• $P_1$:
  $\frac{-1}{39916800}\cdot t^{11}+\frac{11}{3628800}\cdot t^{10}-\frac{11}{72576}\cdot t^9+\frac{11}{2688}\cdot t^8-\frac{11}{168}\cdot t^7+\frac{77}{120}\cdot t^6-\frac{77}{20}\cdot t^5+\frac{55}{4}\cdot t^4-\frac{55}{2}\cdot t^3+\frac{55}{2}\cdot t^2-11\cdot t+1$
• $P_2$:
  $\frac{-1}{39916800}\cdot t^{31}+\frac{1915775589568051119924779058808677305395520485242236102572846315907}{105393851672213585459374657579984306821408885194903283346442293184505600}\cdot t^{30}-\frac{50035361100364010042842434150060563108922023204606835169481390540939}{8130382843285048021151759299027360811937256857892539001011262617090432}\cdot t^{29}+\frac{136700916348577908958856992794866499528894465837494388285553640617071749}{105694976962705624274972870887355690555184339152603007013146414022175616}\cdot t^{28}-\frac{35024931387195200991031229214875963243995709391211051284044028967830196417}{184966209684734842481202524052872458471572593517055262273006224538807328}\cdot t^{27}+\frac{703823921424939641028262461213755110045147264066625294840868295492907788339}{34253001793469415274296763713494899716957887688343567087593745284964320}\cdot t^{26}-\frac{29398875160396445082715047673757192379885395435019300817039279608735875656517}{17126500896734707637148381856747449858478943844171783543796872642482160}\cdot t^{25}+\frac{387774783108723728605957271586394027454196686053987222827218603548500257280815}{3425300179346941527429676371349489971695788768834356708759374528496432}\cdot t^{24}-\frac{855894473265320197282694953160726003842771671506044086667801017476659455672545}{142720840806122563642903182139562082153991198701431529531640605354018}\cdot t^{23}+\frac{36861346878185344379863386467425600041394728992070891216691136517384215792267345}{142720840806122563642903182139562082153991198701431529531640605354018}\cdot t^{22}-\frac{650829715401661567169976996187687494436107612063129176895371896968145404168394649}{71360420403061281821451591069781041076995599350715764765820302677009}\cdot t^{21}+\frac{246127160868024806463905113086329832590826297512739942858930147593797261061014567}{926758706533263400278592091815338195805137653905399542413250684117}\cdot t^{20}-\frac{5018600623040614602443721454878229468530233369077495981717439458586624561587460900}{784180443989684415620347154612978473373578014843030382041981348099}\cdot t^{19}+\frac{1303267164775236207588671083634610748269677942045142728803723332586043123619226876900}{10194345771865897403064513009968720153856514192959394966545757525287}\cdot t^{18}-\frac{799388905378389314973892764913377681147836236090831738134044054355655944373327488200}{377568361920959163076463444813656301994685710850347961723916945381}\cdot t^{17}+\frac{10960528406585622737122349241351486519249514762594625186178453042209555836624122588920}{377568361920959163076463444813656301994685710850347961723916945381}\cdot t^{16}-\frac{124070455639488901130024141572063437939702765903157786918838340573202820744530513409920}{377568361920959163076463444813656301994685710850347961723916945381}\cdot t^{15}+\frac{1154540334666205137317201990147454764363962915617114886531025822960358446139464561712000}{377568361920959163076463444813656301994685710850347961723916945381}\cdot t^{14}-\frac{8780358491574095680552420807487483830342294252849407632635736329968451531539036521184000}{377568361920959163076463444813656301994685710850347961723916945381}\cdot t^{13}+\frac{4166132343257837194840727875240683168183192068594489204058037739747870498080423499808000}{29043720147766089467420264985665869384206593142334458594147457337}\cdot t^{12}-\frac{20643148989045335048670458155578989011248348805989259100569105688442059534020481594649600}{29043720147766089467420264985665869384206593142334458594147457337}\cdot t^{11}+\frac{7380118876415498686635281252124238581948315181679439818553759898908490912737929122329600}{2640338195251462678856387725969624489473326649303132599467950667}\cdot t^{10}-\frac{22689255274398116010652164584613912795961050895039408923053024389228652757247395782400000}{2640338195251462678856387725969624489473326649303132599467950667}\cdot t^9+\frac{53504786447200302297548625836262844569187405851181554687927379690663383173524228972800000}{2640338195251462678856387725969624489473326649303132599467950667}\cdot t^8-\frac{94458956765788626873973968215870144632405268605106019766963770357112521462678859315200000}{2640338195251462678856387725969624489473326649303132599467950667}\cdot t^7+\frac{9304988616876375140293006769762330916486572129086849863411106837017745459641694574592000}{203102938096266359912029825074586499190255896100240969189842359}\cdot t^6-\frac{107713942273291860945018978017179733802900711676628102148947288015934697614821572079616000}{2640338195251462678856387725969624489473326649303132599467950667}\cdot t^5+\frac{62867230892869805269347119693332821141455495828430051154718553772743952853631209164800000}{2640338195251462678856387725969624489473326649303132599467950667}\cdot t^4-\frac{22026250795348979689174298545234742222541459191211571967707136987887419895142826393600000}{2640338195251462678856387725969624489473326649303132599467950667}\cdot t^3+\frac{4007170737327274765880138129420090523831623110746905611395465859151416752973734297600000}{2640338195251462678856387725969624489473326649303132599467950667}\cdot t^2-\frac{283895560754269998506657099247454506060002416956230732446145621340677633894080020480000}{2640338195251462678856387725969624489473326649303132599467950667}\cdot t+\frac{3362577965715373270116662550515268374409776775566331643040225206438487042417786880000}{2640338195251462678856387725969624489473326649303132599467950667}$

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 Laguerre type can be downloaded here packed into a single file.