Rule: Q[3, 10, 26]

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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{13}-\frac{629}{2}\cdot t^{11}+\frac{17435}{4}\cdot t^9-\frac{105435}{4}\cdot t^7+\frac{557865}{8}\cdot t^5-\frac{2248785}{32}\cdot t^3+\frac{1133055}{64}\cdot t$
• $P_3$:
  $8\cdot t^{39}-\frac{62344019653739501860494948964782623868150229}{26776941392753723927870559341744020366902}\cdot t^{37}+\frac{1233581744529904314609470513581742737711841497885}{4070095091698566037036325019945091095769104}\cdot t^{35}-\frac{190450052906489912692065749584619996195644106830795}{8140190183397132074072650039890182191538208}\cdot t^{33}+\frac{41419600209009034562007305677067523168083740727107195}{34595808279437811314808762669533274314037384}\cdot t^{31}-\frac{175066301769333140233457169580343514664197399121933145}{4070095091698566037036325019945091095769104}\cdot t^{29}+\frac{32656934164920136616048366645889400400865811375206961495}{29133312235316051633523168563817494159189376}\cdot t^{27}-\frac{7967956141139620793661276449581133932940071002880897514625}{369021954980669987357960135141688259349732096}\cdot t^{25}+\frac{114538386211271892544993287568588998740273341104219398430375}{369021954980669987357960135141688259349732096}\cdot t^{23}-\frac{2464033845779568995421369434389334031520340661118437410515875}{738043909961339974715920270283376518699464192}\cdot t^{21}+\frac{1040382453979074178554596810680070099133177055887319055650125}{38844416313754735511364224751756658878919168}\cdot t^{19}-\frac{725689826603055442029691917171482693431296825322208578362375}{4569931331029968883689908794324312809284608}\cdot t^{17}+\frac{3131054153930636782252718342535849163501155239635446349149375}{4569931331029968883689908794324312809284608}\cdot t^{15}-\frac{19212891260161469094091188875725761643023079648839047881258125}{9139862662059937767379817588648625618569216}\cdot t^{13}+\frac{648813938120183219863668890785526731072718353449065117001294375}{146237802592959004278077081418378009897107456}\cdot t^{11}-\frac{1796402629495949352845955540848191923720541892375483071865570625}{292475605185918008556154162836756019794214912}\cdot t^9+\frac{1519959679967665559326370237295005468949299028008415630493385625}{292475605185918008556154162836756019794214912}\cdot t^7-\frac{702987496567067711634926914145594171816637244913003162088965625}{292475605185918008556154162836756019794214912}\cdot t^5+\frac{2331205017591749907313626444424796214669956704613057825904496875}{4679609682974688136898466605388096316707438592}\cdot t^3-\frac{274956935804831972811860612795367023122114018353806821174378125}{9359219365949376273796933210776192633414877184}\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.