Rule: Q[8, 42]

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.

• $P_1$:
  $t^8-28\cdot t^6+210\cdot t^4-420\cdot t^2+105$
• $P_2$:
  $t^{50}-\frac{130991759246428165486227056138977322338570461073}{122749103214213163428429988486872850615280185}\cdot t^{48}+\frac{64052612704407332066230912715949943243487766364074}{122749103214213163428429988486872850615280185}\cdot t^{46}-\frac{3812257941826205154866698203721127531750714650393310}{24549820642842632685685997697374570123056037}\cdot t^{44}+\frac{13148790357670704677172786257651880666014268519729363712}{417346950928324755656661960855367692091952629}\cdot t^{42}-\frac{1931072984605241120535598183299741933111107567942337698844}{417346950928324755656661960855367692091952629}\cdot t^{40}+\frac{212760059639063435956518932015205541874425835835677981328174}{417346950928324755656661960855367692091952629}\cdot t^{38}-\frac{486132989187291534170978405279191095834048387890830685534106}{11279647322387155558288161104199126813296017}\cdot t^{36}+\frac{603632567865176765548011767193611077876796983379604098189925}{212823534384663312420531341588662770062189}\cdot t^{34}-\frac{97262501074086957743856442519329959886267632105279207017411605}{663508666022773856369891829658772165488001}\cdot t^{32}+\frac{3966062447380959315807294258890610061864378561986922244926163460}{663508666022773856369891829658772165488001}\cdot t^{30}-\frac{127759646384505441634473759827191961255774841588994260460629744060}{663508666022773856369891829658772165488001}\cdot t^{28}+\frac{3245774506780862138991554577906198066720938943888189592516491463080}{663508666022773856369891829658772165488001}\cdot t^{26}-\frac{64743237334363703395658761644079607729866597806839443267359770940000}{663508666022773856369891829658772165488001}\cdot t^{24}+\frac{1006599016001270100929820601919211994784051094022938861526442714779500}{663508666022773856369891829658772165488001}\cdot t^{22}-\frac{12072895243253553613090504329902640727592255732273672260844735538376500}{663508666022773856369891829658772165488001}\cdot t^{20}+\frac{110164004769635428767904641812725099839702642424260161366629334351995875}{663508666022773856369891829658772165488001}\cdot t^{18}-\frac{751046361658732995204816423996874505270101364211310885979169523548013875}{663508666022773856369891829658772165488001}\cdot t^{16}+\frac{3736249336971282327123914648396717738189372070357171784397922962631281250}{663508666022773856369891829658772165488001}\cdot t^{14}-\frac{13147634508167428736095647882216196212502839168922642144023755772528198750}{663508666022773856369891829658772165488001}\cdot t^{12}+\frac{31382187878989442031350470803455981092839027111567283504691562690267735000}{663508666022773856369891829658772165488001}\cdot t^{10}-\frac{47893841565017354587142777288015819269303680384821029628820299844432472500}{663508666022773856369891829658772165488001}\cdot t^8+\frac{42755198886194678540028162517084834573932383581846320298470905609531898750}{663508666022773856369891829658772165488001}\cdot t^6-\frac{19241947922280145641690569666403275933075274038285707667192025296486531250}{663508666022773856369891829658772165488001}\cdot t^4+\frac{3247398975199601167248431400156602164593303084321037179212261548160071875}{663508666022773856369891829658772165488001}\cdot t^2-\frac{84159669392864016658268201230066290441059327904791805855537630959409375}{663508666022773856369891829658772165488001}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.