Rule: Q[50]

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}{30414093201713378043612608166064768844377641568960512000000000000}\cdot t^{50}-\frac{1}{12165637280685351217445043266425907537751056627584204800000000}\cdot t^{49}+\frac{1}{10133808646968222588459011467243571460017539881369600000000}\cdot t^{48}-\frac{1}{13195063342406539828722671181306733671897838387200000000}\cdot t^{47}+\frac{47}{1122984114247365091806184781387807121012581990400000000}\cdot t^{46}-\frac{47}{2653554145196987457008943245245290928668672000000000}\cdot t^{45}+\frac{47}{7862382652435518391137609615541602751610880000000}\cdot t^{44}-\frac{47}{28428036449921812364650447990078109122560000000}\cdot t^{43}+\frac{2021}{5288937013938941835283804277223834255360000000}\cdot t^{42}-\frac{2021}{26984372520096642016754103455223644160000000}\cdot t^{41}+\frac{82861}{6581554273194302930915634989078937600000000}\cdot t^{40}-\frac{82861}{45248185628210832650044990549917696000000}\cdot t^{39}+\frac{82861}{356987657816259034714358899802112000000}\cdot t^{38}-\frac{82861}{3213877805825046711417358516224000000}\cdot t^{37}+\frac{3065857}{1216061872474341998914676195328000000}\cdot t^{36}-\frac{3065857}{14074790190675254617068011520000000}\cdot t^{35}+\frac{3065857}{183833994327186999080071987200000}\cdot t^{34}-\frac{3065857}{2703441093046867633530470400000}\cdot t^{33}+\frac{3065857}{44684976744576324521164800000}\cdot t^{32}-\frac{3065857}{829115779440381021388800000}\cdot t^{31}+\frac{95041567}{534913406090568400896000000}\cdot t^{30}-\frac{95041567}{12481312808779929354240000}\cdot t^{29}+\frac{2756205443}{9468582130798567096320000}\cdot t^{28}-\frac{2756205443}{277777281898427351040000}\cdot t^{27}+\frac{2756205443}{9144931091306250240000}\cdot t^{26}-\frac{2756205443}{338200114323456000000}\cdot t^{25}+\frac{2756205443}{14069124755855769600}\cdot t^{24}-\frac{2756205443}{659490222930739200}\cdot t^{23}+\frac{63392725189}{802857662698291200}\cdot t^{22}-\frac{2185956041}{1658796823756800}\cdot t^{21}+\frac{2185956041}{112843321344000}\cdot t^{20}-\frac{70514711}{282108303360}\cdot t^{19}+\frac{1339779509}{475129774080}\cdot t^{18}-\frac{1339779509}{48392847360}\cdot t^{17}+\frac{1339779509}{5693276160}\cdot t^{16}-\frac{1339779509}{778377600}\cdot t^{15}+\frac{1339779509}{124540416}\cdot t^{14}-\frac{253471799}{4447872}\cdot t^{13}+\frac{173428073}{684288}\cdot t^{12}-\frac{13340621}{14256}\cdot t^{11}+\frac{146746831}{51840}\cdot t^{10}-\frac{17895955}{2592}\cdot t^9+\frac{2556565}{192}\cdot t^8-\frac{59455}{3}\cdot t^7+\frac{264845}{12}\cdot t^6-\frac{52969}{3}\cdot t^5+\frac{57575}{6}\cdot t^4-\frac{9800}{3}\cdot t^3+\frac{1225}{2}\cdot t^2-50\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.