Rule: Q[1, 31]

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^{32}+\frac{1778915425493405355440676172074738689}{1776683398289895606164919649702140}\cdot t^{31}-\frac{835352638071788631685952056281580531649}{1776683398289895606164919649702140}\cdot t^{30}+\frac{8159364141939959900826592118812491232335}{59222779942996520205497321656738}\cdot t^{29}-\frac{1674683700139817540177867787628629495404845}{59222779942996520205497321656738}\cdot t^{28}+\frac{128094709411841867278624455250511524402162490}{29611389971498260102748660828369}\cdot t^{27}-\frac{15174647333025727787987445228039027308297093538}{29611389971498260102748660828369}\cdot t^{26}+\frac{1427884618774080577470926420109035910795779501388}{29611389971498260102748660828369}\cdot t^{25}-\frac{108619677072675626115105545841206699673349082452500}{29611389971498260102748660828369}\cdot t^{24}+\frac{6763895571432077255378877767129278004209785046980000}{29611389971498260102748660828369}\cdot t^{23}-\frac{347877372760263173843783931762288210431304604419300000}{29611389971498260102748660828369}\cdot t^{22}+\frac{14869565470837856278633110104311255035356109513547752000}{29611389971498260102748660828369}\cdot t^{21}-\frac{530395350353236884374134975007257208831254503899751672000}{29611389971498260102748660828369}\cdot t^{20}+\frac{15825666758559463092569327805571562926559137943896106400000}{29611389971498260102748660828369}\cdot t^{19}-\frac{395333074751822607050717694461795322381598452627937984800000}{29611389971498260102748660828369}\cdot t^{18}+\frac{8263944606668503095261105079554927992875229294146615281600000}{29611389971498260102748660828369}\cdot t^{17}-\frac{144295799801476084175469912504652328715437021958256472278080000}{29611389971498260102748660828369}\cdot t^{16}+\frac{2098057037477682163844308547912941486073452646264315573191680000}{29611389971498260102748660828369}\cdot t^{15}-\frac{25289863621370085310136906638124275275989347317406671018624000000}{29611389971498260102748660828369}\cdot t^{14}+\frac{251230884092460638955532182092526803542519219214517993946368000000}{29611389971498260102748660828369}\cdot t^{13}-\frac{2041324460651367151472244152413101679232071803299621016585984000000}{29611389971498260102748660828369}\cdot t^{12}+\frac{13438271662089887340138797939275555669919013971907874178229657600000}{29611389971498260102748660828369}\cdot t^{11}-\frac{70833894338422913886002140726736991895213874252258051906426265600000}{29611389971498260102748660828369}\cdot t^{10}+\frac{294596932762397597396699533858514902634231181126186068837345280000000}{29611389971498260102748660828369}\cdot t^9-\frac{949118890093238850404864353750465385623030796074056289938216960000000}{29611389971498260102748660828369}\cdot t^8+\frac{2314171218210267672565421518664814015630160270968920569729007616000000}{29611389971498260102748660828369}\cdot t^7-\frac{4143511761973475019870197088257438290738566288285561339368954265600000}{29611389971498260102748660828369}\cdot t^6+\frac{5234267791298337696284338162810815607821927882737029832331499929600000}{29611389971498260102748660828369}\cdot t^5-\frac{4414154672588132767328940661855696572612292304547599296581304320000000}{29611389971498260102748660828369}\cdot t^4+\frac{2292334322807428424892851684603913652625422108103247582271242240000000}{29611389971498260102748660828369}\cdot t^3-\frac{644781889256076458964024280524163931280804883419587286480322560000000}{29611389971498260102748660828369}\cdot t^2+\frac{77659804086441856833573297505439195712772017342993586874744832000000}{29611389971498260102748660828369}\cdot t-\frac{2253810782595856136920813833911869363980489457245214959992832000000}{29611389971498260102748660828369}$

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.