Rule: Q[1, 3, 20]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^4+\frac{49}{4}\cdot t^3-\frac{153}{4}\cdot t^2+\frac{57}{2}\cdot t-\frac{3}{2}$
• $P_3$:
  $-t^{24}+\frac{54782894377735845569395894066993400119198300043552139913917413780161777}{108274031606943837114186276598942891675900278703290455144610192690692}\cdot t^{23}-\frac{12676151202859883934616802815498572315327890052366924773297013069372919369}{108274031606943837114186276598942891675900278703290455144610192690692}\cdot t^{22}+\frac{15140901796343237210288974758666587503769167781595557840508919910617804081037}{920329268659022615470583351091014579245152368977968868729186637870882}\cdot t^{21}-\frac{1447208360663143933773753701028260571268827154317445453590076727781305557829823}{920329268659022615470583351091014579245152368977968868729186637870882}\cdot t^{20}+\frac{2937546591504330580309848744528781425530971756419160650957076552977832036877910}{27068507901735959278546569149735722918975069675822613786152548172673}\cdot t^{19}-\frac{2578236967486286804326051146802668218870076368887002999471811829399775850397576670}{460164634329511307735291675545507289622576184488984434364593318935441}\cdot t^{18}+\frac{101818546985335799465477481427865239749324631531303145682457378597813098907961342340}{460164634329511307735291675545507289622576184488984434364593318935441}\cdot t^{17}-\frac{183477748235824394627606179453493246929927801047427350892216581787840034693456572860}{27068507901735959278546569149735722918975069675822613786152548172673}\cdot t^{16}+\frac{4396606202789971742542793683250440697397611316526733468575645009294981794728785146240}{27068507901735959278546569149735722918975069675822613786152548172673}\cdot t^{15}-\frac{82747751260141401120969308157981653769719962992890809853950261169697454595703421526400}{27068507901735959278546569149735722918975069675822613786152548172673}\cdot t^{14}+\frac{174847689646127195253558412831692202870830675797330079656439657689404313134133054803200}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^{13}-\frac{2027379926895947152196030676619019281971925526896751470168463955446256582596855696582400}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^{12}+\frac{18327370890772000047201697270156334628134819250309577629710331659852386964781630776755200}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^{11}-\frac{128067388929099517917864508004988329657868916743458323782936617806512439480080636078412800}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^{10}+\frac{683555506398611500029075583085452640762230184518778606953249784572432045609080842226432000}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^9-\frac{2743097733791552257819388501020280781173334486543776572800365276071740679756640700579072000}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^8+\frac{8108260914039856840203295284680942630407918895087959713521479229287104475572963516785664000}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^7-\frac{17191233810064106404872771235146949722069455264721747746141197964217321933123487404475392000}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^6+\frac{25252851972032608234654324472466380485121274043228397091136902118776042151376466072987648000}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^5-\frac{24525314832081964406499450576051328788267350900578943219930113942997418737670683105064960000}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^4+\frac{14722811096463254887910768138871263673259495584659385207523555781443126500814225123368960000}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^3-\frac{4900517652350925509124984271363642424569655228240776690843433424644098149057957001912320000}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t^2+\frac{732574785994769382417138749811775903356111348299610444942182708816985093537944206786560000}{3866929700247994182649509878533674702710724239403230540878935453239}\cdot t-\frac{28286477967511376458807702544522327891422378500654021951225926616395731208572371517440000}{3866929700247994182649509878533674702710724239403230540878935453239}$

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.