Rule: Q[6, 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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{42}-\frac{24276646141048335638046496013160}{962803001092348035361314161}\cdot t^{40}+\frac{133809641261445778193082920987236950}{29846893033862789096200738991}\cdot t^{38}-\frac{14238310080101542043226848882662613613}{29846893033862789096200738991}\cdot t^{36}+\frac{2027739466444894952486144733975716621415}{59693786067725578192401477982}\cdot t^{34}-\frac{204740627388926662504588724585108106720975}{119387572135451156384802955964}\cdot t^{32}+\frac{122188790921062616387547693334929856949085}{1925606002184696070722628322}\cdot t^{30}-\frac{6758083653471907364204167090343617990471275}{3851212004369392141445256644}\cdot t^{28}+\frac{282380438285173669280935109108025915887491665}{7702424008738784282890513288}\cdot t^{26}-\frac{559570123656432387305792682312529545964707375}{962803001092348035361314161}\cdot t^{24}+\frac{430457897470113219644110809745424734716142720875}{61619392069910274263124106304}\cdot t^{22}-\frac{7802777702128209494428135437857562233774591434125}{123238784139820548526248212608}\cdot t^{20}+\frac{105557770700905948695271613258382192106774018269375}{246477568279641097052496425216}\cdot t^{18}-\frac{1049234031024426376596218242645910173164183191629875}{492955136559282194104992850432}\cdot t^{16}+\frac{3747884391564568983101410836414769740312460754645625}{492955136559282194104992850432}\cdot t^{14}-\frac{18666405766587398776758995542743006134023305948519375}{985910273118564388209985700864}\cdot t^{12}+\frac{62131956997532428823017621627284467004127650489226875}{1971820546237128776419971401728}\cdot t^{10}-\frac{260296745481186468807134991322551447173924756305284375}{7887282184948515105679885606912}\cdot t^8+\frac{627229620803636210203093774928277027686973917499148125}{31549128739794060422719542427648}\cdot t^6-\frac{375179883534611341500122406476328619474372472126596875}{63098257479588120845439084855296}\cdot t^4+\frac{83707624737910196500364428937573890044338298607940625}{126196514959176241690878169710592}\cdot t^2-\frac{2948887721619820238294005934732940088412922491690625}{252393029918352483381756339421184}$

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.