Rule: Q[1, 5, 14]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^6+\frac{1831}{56}\cdot t^5-\frac{20575}{56}\cdot t^4+\frac{12175}{7}\cdot t^3-\frac{23925}{7}\cdot t^2+\frac{16365}{7}\cdot t-\frac{2265}{7}$
• $P_3$:
  $-t^{20}+\frac{17239261096906571440164201121282246570910097682008727604217823239013}{56264940340587715043400028903977632338247906466191932088638723880}\cdot t^{19}-\frac{7091923313098679990129670003575803778097626388992824980001053597527299}{168794821021763145130200086711932897014743719398575796265916171640}\cdot t^{18}+\frac{288511186924991866591632944678951931976769463617908956176036813228903479}{84397410510881572565100043355966448507371859699287898132958085820}\cdot t^{17}-\frac{15570682450106490784756502781683489748242120685115939273406845254534904297}{84397410510881572565100043355966448507371859699287898132958085820}\cdot t^{16}+\frac{295195638355380666235315908609788568832940785460942902570723120654708129259}{42198705255440786282550021677983224253685929849643949066479042910}\cdot t^{15}-\frac{1625329055863301282026419618985182831482294846387192045116221178233137645095}{8439741051088157256510004335596644850737185969928789813295808582}\cdot t^{14}+\frac{215026956987734252730945078948535824397729751844829008735538919043111182155}{54803513318754267899415612568809382147644064739797336449972783}\cdot t^{13}-\frac{36027687991463861699890713493990816511981745452179455530364037240299880992835}{602838646506296946893571738256903203624084712137770700949700613}\cdot t^{12}+\frac{137229971717328560949666895693304001437555161816475056664387988906676431113860}{200946215502098982297857246085634401208028237379256900316566871}\cdot t^{11}-\frac{106712381909429091998240908235217816595636461896326000265239674878362725709340}{18267837772918089299805204189603127382548021579932445483324261}\cdot t^{10}+\frac{678078714962247921812240405192306802037248050158246374093248186157850269848680}{18267837772918089299805204189603127382548021579932445483324261}\cdot t^9-\frac{3158042683580151374470609239280583376395852074493536875025631553188203104886680}{18267837772918089299805204189603127382548021579932445483324261}\cdot t^8+\frac{10564633939831315131198143038482394970254586002574043686329742261254593462087360}{18267837772918089299805204189603127382548021579932445483324261}\cdot t^7-\frac{24665626132593713399284652150003838701222337824494844914731828225816873275878080}{18267837772918089299805204189603127382548021579932445483324261}\cdot t^6+\frac{38595681144210070661961637013663991324959020437008470731569691198429435443560320}{18267837772918089299805204189603127382548021579932445483324261}\cdot t^5-\frac{38200880038691311460875975443929319978067724646717855185619554787174118220918400}{18267837772918089299805204189603127382548021579932445483324261}\cdot t^4+\frac{21960405241889805623352404797119764362228628838107275399947388540803514643750400}{18267837772918089299805204189603127382548021579932445483324261}\cdot t^3-\frac{6431428996526799651048867740064713249773072143720675079119693080544226376332800}{18267837772918089299805204189603127382548021579932445483324261}\cdot t^2+\frac{778294538200691437819120387378087702708265620090142987014089756123853466342400}{18267837772918089299805204189603127382548021579932445483324261}\cdot t-\frac{25855331751873156282252075685402362298884220770692273487826318868685814041600}{18267837772918089299805204189603127382548021579932445483324261}$

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.