Rule: Q[6, 41]

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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{47}-\frac{16470982152114965354219522983265090891465}{16188442151594219121643968296810508779}\cdot t^{45}+\frac{206441275574776077970493681373244035516205}{437525463556600516801188332346229967}\cdot t^{43}-\frac{15002912513351881254651406712571902556159739305}{113319095061159533851507778077673561453}\cdot t^{41}+\frac{2851748523358935860198316860000541879028042878075}{113319095061159533851507778077673561453}\cdot t^{39}-\frac{389592644907429662628234794075108432099955966619185}{113319095061159533851507778077673561453}\cdot t^{37}+\frac{1070577821541427234295366137199953464168653247574725}{3062678244896203617608318326423609769}\cdot t^{35}-\frac{11824505386910208941266386109693601651191263387707925}{437525463556600516801188332346229967}\cdot t^{33}+\frac{704366437091541761298460083940732905504371912167228950}{437525463556600516801188332346229967}\cdot t^{31}-\frac{32562203723098889868657100536032116767237879287450387250}{437525463556600516801188332346229967}\cdot t^{29}+\frac{3058452494657594488007284599773251028477444594121011550}{1142364134612533986426079196726449}\cdot t^{27}-\frac{32752923847290295580709923564290400824745501909176931790750}{437525463556600516801188332346229967}\cdot t^{25}+\frac{708407092800730243209283890345507435536564235698926773251250}{437525463556600516801188332346229967}\cdot t^{23}-\frac{11752130683549723878153189379312682561390788428733032866973750}{437525463556600516801188332346229967}\cdot t^{21}+\frac{147672183561111439356485857223733242301779318146705410940443750}{437525463556600516801188332346229967}\cdot t^{19}-\frac{1381282459312277905297248956459989884239526278744493168376466250}{437525463556600516801188332346229967}\cdot t^{17}+\frac{9394927236451280538775336638150443127911117408636503629154696875}{437525463556600516801188332346229967}\cdot t^{15}-\frac{45028446568573706963240603727893085176750713286060222262812315625}{437525463556600516801188332346229967}\cdot t^{13}+\frac{145757518145355264926601197884629965623903839654680295194604590625}{437525463556600516801188332346229967}\cdot t^{11}-\frac{300643198216446261764642514833742816220412196165499414919380359375}{437525463556600516801188332346229967}\cdot t^9+\frac{364370741402025414221528140380709816134443203958022651197775103125}{437525463556600516801188332346229967}\cdot t^7-\frac{231735035799038062654492104636697525475208702693831741888999609375}{437525463556600516801188332346229967}\cdot t^5+\frac{66306062691762510099444243724060850693187666582382796261315484375}{437525463556600516801188332346229967}\cdot t^3-\frac{6486660812951389248492850895671098532993880187519949428960140625}{437525463556600516801188332346229967}\cdot t$

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.