Rule: Q[47]

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}{258623241511168180642964355153611979969197632389120000000000}\cdot t^{47}+\frac{47}{5502622159812088949850305428800254892961651752960000000000}\cdot t^{46}-\frac{47}{5200966124586095415737528760680770220190597120000000000}\cdot t^{45}+\frac{47}{7705134999386808023314857423230770696578662400000000}\cdot t^{44}-\frac{47}{15919700411956214924204250874443741108633600000000}\cdot t^{43}+\frac{2021}{1851127954878629642349331497028341989376000000000}\cdot t^{42}-\frac{2021}{6296353588022549803909290806218850304000000000}\cdot t^{41}+\frac{82861}{1074987197955069478716220381549559808000000000}\cdot t^{40}-\frac{82861}{5374935989775347393581101907747799040000000}\cdot t^{39}+\frac{82861}{31804354969084895820006520164188160000000}\cdot t^{38}-\frac{82861}{220251765713884320083147646566400000000}\cdot t^{37}+\frac{3065857}{65480254671695338403097948979200000000}\cdot t^{36}-\frac{3065857}{606298654367549429658314342400000000}\cdot t^{35}+\frac{3065857}{6434189801451544967802519552000000}\cdot t^{34}-\frac{3065857}{77922713858409714142937088000000}\cdot t^{33}+\frac{3065857}{1073315617884431324282880000000}\cdot t^{32}-\frac{3065857}{16770556529444239441920000000}\cdot t^{31}+\frac{95041567}{9196756806469421629440000000}\cdot t^{30}-\frac{95041567}{183935136129388432588800000}\cdot t^{29}+\frac{2756205443}{120509227119254490316800000}\cdot t^{28}-\frac{2756205443}{3074214977532002304000000}\cdot t^{27}+\frac{2756205443}{88557633097629696000000}\cdot t^{26}-\frac{2756205443}{2882053148147712000000}\cdot t^{25}+\frac{2756205443}{106059555851835801600}\cdot t^{24}-\frac{2756205443}{4419148160493158400}\cdot t^{23}+\frac{63392725189}{4803421913579520000}\cdot t^{22}-\frac{63392725189}{258035061473280000}\cdot t^{21}+\frac{63392725189}{15798064988160000}\cdot t^{20}-\frac{63392725189}{1105864549171200}\cdot t^{19}+\frac{41533164779}{58203397324800}\cdot t^{18}-\frac{41533164779}{5389203456000}\cdot t^{17}+\frac{22776251653}{317011968000}\cdot t^{16}-\frac{22776251653}{39626496000}\cdot t^{15}+\frac{22776251653}{5811886080}\cdot t^{14}-\frac{1339779509}{59304960}\cdot t^{13}+\frac{17417133617}{159667200}\cdot t^{12}-\frac{17417133617}{39916800}\cdot t^{11}+\frac{5178066751}{3628800}\cdot t^{10}-\frac{272529829}{72576}\cdot t^9+\frac{20963833}{2688}\cdot t^8-\frac{20963833}{1680}\cdot t^7+\frac{3579191}{240}\cdot t^6-\frac{511313}{40}\cdot t^5+\frac{59455}{8}\cdot t^4-\frac{5405}{2}\cdot t^3+\frac{1081}{2}\cdot t^2-47\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.