Rule: Q[48]

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}{12413915592536072670862289047373375038521486354677760000000000}\cdot t^{48}-\frac{1}{5387984198149337096728424065700249582691617341440000000000}\cdot t^{47}+\frac{47}{229275923325503706243762726200010620540068823040000000000}\cdot t^{46}-\frac{47}{325060382786630963483595547542548138761912320000000000}\cdot t^{45}+\frac{47}{642094583282234001942904785269230891381555200000000}\cdot t^{44}-\frac{47}{1658302126245439054604609466087889698816000000000}\cdot t^{43}+\frac{2021}{231390994359828705293666437128542748672000000000}\cdot t^{42}-\frac{2021}{918218231586621846403438242573582336000000000}\cdot t^{41}+\frac{82861}{179164532992511579786036730258259968000000000}\cdot t^{40}-\frac{82861}{1007800498082877636296456607702712320000000}\cdot t^{39}+\frac{82861}{6625907285226019962501358367539200000000}\cdot t^{38}-\frac{82861}{50474362976098490019054669004800000000}\cdot t^{37}+\frac{3065857}{16370063667923834600774487244800000000}\cdot t^{36}-\frac{3065857}{164205885557877970532460134400000000}\cdot t^{35}+\frac{3065857}{1876638692090033948942401536000000}\cdot t^{34}-\frac{3065857}{24350848080753035669667840000000}\cdot t^{33}+\frac{3065857}{357771872628143774760960000000}\cdot t^{32}-\frac{3065857}{5939572104178168135680000000}\cdot t^{31}+\frac{95041567}{3448783802426033111040000000}\cdot t^{30}-\frac{95041567}{72807658051216254566400000}\cdot t^{29}+\frac{2756205443}{50212177966356037632000000}\cdot t^{28}-\frac{2756205443}{1344969052670251008000000}\cdot t^{27}+\frac{2756205443}{40588915169746944000000}\cdot t^{26}-\frac{2756205443}{1380983800154112000000}\cdot t^{25}+\frac{2756205443}{53029777925917900800}\cdot t^{24}-\frac{2756205443}{2301639666923520000}\cdot t^{23}+\frac{63392725189}{2601853536522240000}\cdot t^{22}-\frac{63392725189}{145144722078720000}\cdot t^{21}+\frac{63392725189}{9215537909760000}\cdot t^{20}-\frac{2185956041}{23038844774400}\cdot t^{19}+\frac{41533164779}{36377123328000}\cdot t^{18}-\frac{1339779509}{112275072000}\cdot t^{17}+\frac{22776251653}{211341312000}\cdot t^{16}-\frac{22776251653}{27243216000}\cdot t^{15}+\frac{1339779509}{242161920}\cdot t^{14}-\frac{1339779509}{43243200}\cdot t^{13}+\frac{17417133617}{119750400}\cdot t^{12}-\frac{470733341}{831600}\cdot t^{11}+\frac{272529829}{151200}\cdot t^{10}-\frac{20963833}{4536}\cdot t^9+\frac{20963833}{2240}\cdot t^8-\frac{511313}{35}\cdot t^7+\frac{511313}{30}\cdot t^6-\frac{71346}{5}\cdot t^5+\frac{16215}{2}\cdot t^4-\frac{8648}{3}\cdot t^3+564\cdot t^2-48\cdot t+1$

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.