Rule: Q[1, 6, 50]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-21\cdot t^5+105\cdot t^3-105\cdot t$
• $P_3$:
  $t^{57}-\frac{9486404713707924363988176269132286335371473938329}{6536537506862970963870041612472645306620540974}\cdot t^{55}+\frac{19164546566724001585274782691598315282298498199076535}{19609612520588912891610124837417935919861622922}\cdot t^{53}-\frac{29193611267589114648740094774150568181880571547559779295}{71901912575492680602570457737199098372825950714}\cdot t^{51}+\frac{8392485544137589723242753689303636583766799144716553352625}{71901912575492680602570457737199098372825950714}\cdot t^{49}-\frac{38586693140491090221676977875332259421111340783207621031275}{1563085055988971317447183863852154312452738059}\cdot t^{47}+\frac{6232289163141975104853664083976313680653778417881825688418775}{1563085055988971317447183863852154312452738059}\cdot t^{45}-\frac{71606301945491080220021565020310287064749256622190228384318625}{142098641453542847040653078532014028404794369}\cdot t^{43}+\frac{7199313140612621264755613409651732397623807239015457436119516750}{142098641453542847040653078532014028404794369}\cdot t^{41}-\frac{1164615220822154136272980955265146437853463023273457814909947283125}{284197282907085694081306157064028056809588738}\cdot t^{39}+\frac{76350574765417696626481465593316954144812062190239006964438656243625}{284197282907085694081306157064028056809588738}\cdot t^{37}-\frac{4075795438051680668407164136075323112750092012976863036776450275208625}{284197282907085694081306157064028056809588738}\cdot t^{35}+\frac{177572033272013828746858248207215732055908875045185019593674784824251875}{284197282907085694081306157064028056809588738}\cdot t^{33}-\frac{3157848017548020515038585142076379194631302216357946960361088754770333750}{142098641453542847040653078532014028404794369}\cdot t^{31}+\frac{91548180120684036047253636691555502850654331278952549844575456828709868750}{142098641453542847040653078532014028404794369}\cdot t^{29}-\frac{2156134129887723551005715158994639449798968863007438180166449380146698603750}{142098641453542847040653078532014028404794369}\cdot t^{27}+\frac{41042193613416579476634872922767410951468304119791546274719557848181014625625}{142098641453542847040653078532014028404794369}\cdot t^{25}-\frac{1253831142573620794499997880842264349103064464633169632934147336259223339015625}{284197282907085694081306157064028056809588738}\cdot t^{23}+\frac{15224374409652672275660689882277440055572248428813870234892569684654184013078125}{284197282907085694081306157064028056809588738}\cdot t^{21}-\frac{145162176967367365062133128144079667183732984849799779612438010781117651206328125}{284197282907085694081306157064028056809588738}\cdot t^{19}+\frac{1069897128374408161656526914555902583678039725188314016773491188760092606272796875}{284197282907085694081306157064028056809588738}\cdot t^{17}-\frac{2986110380104523241970389556185864412846849952632336545894968388094105195570265625}{142098641453542847040653078532014028404794369}\cdot t^{15}+\frac{12289220988841566935170670729354818350881215751686497352013437423810562783181328125}{142098641453542847040653078532014028404794369}\cdot t^{13}-\frac{35959472704321700716862604579546944218336349629341403221880561259262241830873515625}{142098641453542847040653078532014028404794369}\cdot t^{11}+\frac{71120732156563523760106675390363165774279733725833699743850010603435024178353125000}{142098641453542847040653078532014028404794369}\cdot t^9-\frac{176580526496200316084417499422523508489665223819475281897557244700590807145551921875}{284197282907085694081306157064028056809588738}\cdot t^7+\frac{122463203540870776731868272354616512674335354101420905795428808846992256027234109375}{284197282907085694081306157064028056809588738}\cdot t^5-\frac{38583638692680639631987824976547091793239227202576336739486211715983009372662734375}{284197282907085694081306157064028056809588738}\cdot t^3+\frac{3451477926405291624802425198377682914298993076555670896287536604504143207440078125}{284197282907085694081306157064028056809588738}\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.