Rule: Q[2, 3, 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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{41}-\frac{300485341728498038566567469904881468758}{201055517588041462530306433067873447}\cdot t^{39}+\frac{50543970073899062469657084528036329598177}{201055517588041462530306433067873447}\cdot t^{37}-\frac{10149808554700615983939299074490427271306035}{402111035176082925060612866135746894}\cdot t^{35}+\frac{40008287883114330640418466174753765009109665}{23653590304475466180036050949161582}\cdot t^{33}-\frac{1895491345607474818141305392225889332881601595}{23653590304475466180036050949161582}\cdot t^{31}+\frac{131266943451154149928549714612306924867698414885}{47307180608950932360072101898323164}\cdot t^{29}-\frac{6775154378010846941806504216426646845273178133855}{94614361217901864720144203796646328}\cdot t^{27}+\frac{526960562196274658483589386430665441052531523191525}{378457444871607458880576815186585312}\cdot t^{25}-\frac{15513513509070585469385323227900587841786050279815125}{756914889743214917761153630373170624}\cdot t^{23}+\frac{345643814840630251973900713604183984495984827414014375}{1513829779486429835522307260746341248}\cdot t^{21}-\frac{5800947917589203542224405725272662748422356238006805125}{3027659558972859671044614521492682496}\cdot t^{19}+\frac{4542104526503841887323086953653797825463020147788404125}{378457444871607458880576815186585312}\cdot t^{17}-\frac{335089994690656135852498939288513422546926870586916359375}{6055319117945719342089229042985364992}\cdot t^{15}+\frac{2229345663790954390638664594220329373215450029886719875625}{12110638235891438684178458085970729984}\cdot t^{13}-\frac{10397692150840660519443347589807063886481874369944967076875}{24221276471782877368356916171941459968}\cdot t^{11}+\frac{130402165991881882485947088812746057603452820701762376314375}{193770211774263018946855329375531679744}\cdot t^9-\frac{257717460101339943447813946260953656259052327844145734861875}{387540423548526037893710658751063359488}\cdot t^7+\frac{288716657539005346582007637954959922577755326291048840915625}{775080847097052075787421317502126718976}\cdot t^5-\frac{150688904957231736995270509700047923324982247789190076396875}{1550161694194104151574842635004253437952}\cdot t^3+\frac{11583440358846110334847444555125236612685284842502905396875}{1550161694194104151574842635004253437952}\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.