Rule: Q[45]

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}{119622220865480194561963161495657715064383733760000000000}\cdot t^{45}+\frac{1}{59072701661965528178747240244769242007103078400000000}\cdot t^{44}-\frac{1}{61025518245832157209449628352034340916428800000000}\cdot t^{43}+\frac{43}{4257594296220848177403462443165186575564800000000}\cdot t^{42}-\frac{43}{9654408834967909699327579236202237132800000000}\cdot t^{41}+\frac{1763}{1177366931093647524308241370268565504000000000}\cdot t^{40}-\frac{1763}{4415125991601178216155905138507120640000000}\cdot t^{39}+\frac{1763}{20319449008026461218337498993786880000000}\cdot t^{38}-\frac{1763}{112573124698207541375831019356160000000}\cdot t^{37}+\frac{65231}{27382651953618050604931869573120000000}\cdot t^{36}-\frac{65231}{211285894703842983062745907200000000}\cdot t^{35}+\frac{65231}{1897261095299814541787922432000000}\cdot t^{34}-\frac{65231}{19694751854323334343819264000000}\cdot t^{33}+\frac{65231}{235107230584208766271488000000}\cdot t^{32}-\frac{65231}{3214356668143479226368000000}\cdot t^{31}+\frac{2022161}{1555333871682328657920000000}\cdot t^{30}-\frac{2022161}{27650379941019176140800000}\cdot t^{29}+\frac{58642669}{16208843413700896358400000}\cdot t^{28}-\frac{58642669}{372141813069663436800000}\cdot t^{27}+\frac{58642669}{9699169339264204800000}\cdot t^{26}-\frac{58642669}{286957672759296000000}\cdot t^{25}+\frac{58642669}{9641777804712345600}\cdot t^{24}-\frac{58642669}{368262346707763200}\cdot t^{23}+\frac{58642669}{16011406378598400}\cdot t^{22}-\frac{58642669}{793954035302400}\cdot t^{21}+\frac{58642669}{45008732160000}\cdot t^{20}-\frac{58642669}{2925567590400}\cdot t^{19}+\frac{1114210711}{4157385523200}\cdot t^{18}-\frac{1114210711}{359280230400}\cdot t^{17}+\frac{653158003}{21134131200}\cdot t^{16}-\frac{653158003}{2476656000}\cdot t^{15}+\frac{21069613}{11007360}\cdot t^{14}-\frac{21069613}{1797120}\cdot t^{13}+\frac{273904969}{4561920}\cdot t^{12}-\frac{16112057}{63360}\cdot t^{11}+\frac{177232627}{201600}\cdot t^{10}-\frac{177232627}{72576}\cdot t^9+\frac{4790071}{896}\cdot t^8-\frac{252109}{28}\cdot t^7+\frac{135751}{12}\cdot t^6-\frac{407253}{40}\cdot t^5+\frac{49665}{8}\cdot t^4-2365\cdot t^3+495\cdot t^2-45\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.