Rule: Q[1, 4, 56]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_3$:
  $t^{61}-\frac{1488698946934398188033760927573771790176396393566}{869747000783558979970315732869543405757899861}\cdot t^{59}+\frac{15451323782868840253307478774649100978278280505809309}{11306711010186266739614104527304064274852698193}\cdot t^{57}-\frac{2551058167179620438349384972742307373223883185705265260}{3768903670062088913204701509101354758284232731}\cdot t^{55}+\frac{1843875909873810047181407122422860823642772935906228635}{7901265555685720992043399390149590688226903}\cdot t^{53}-\frac{36203701981257333883620619729973002871540389791223548950}{607789658129670845541799953088430052940531}\cdot t^{51}+\frac{7104524789780551725113958878990540526441162683011418771475}{607789658129670845541799953088430052940531}\cdot t^{49}-\frac{1098783055485632006630443068465641803550166514408983048391800}{607789658129670845541799953088430052940531}\cdot t^{47}+\frac{136225030077824242056945151147516656506629406165660079899778375}{607789658129670845541799953088430052940531}\cdot t^{45}-\frac{13698929900567225181431473258278015228612833196402904938763949250}{607789658129670845541799953088430052940531}\cdot t^{43}+\frac{1126453347454579727886235855371893835374113352402793144211343692875}{607789658129670845541799953088430052940531}\cdot t^{41}-\frac{1857169374660192869746468448720818417766315337720607378849774228500}{14824138003162703549799998855815367144891}\cdot t^{39}+\frac{103513522988254305850290077338888588004066961206115386106502186759875}{14824138003162703549799998855815367144891}\cdot t^{37}-\frac{4762921120072191359610883657037658720083509090669046614340744687463750}{14824138003162703549799998855815367144891}\cdot t^{35}+\frac{180824174189963282809991480176352741258971989798260184560678669785299375}{14824138003162703549799998855815367144891}\cdot t^{33}-\frac{5652446610655000310005655568877752542568042543793300386893171737189290000}{14824138003162703549799998855815367144891}\cdot t^{31}+\frac{144953201275424224422236436449157293883796939085681345240525300414312630625}{14824138003162703549799998855815367144891}\cdot t^{29}-\frac{104604743069747753455174998893466094479903020557153034036977927903500648750}{511177172522851846544827546752254039479}\cdot t^{27}+\frac{1774094695596567023909655387331844164806036522237100173451113743929573640625}{511177172522851846544827546752254039479}\cdot t^{25}-\frac{24168702576549465023676255886989439017140129777456121127147670575991525062500}{511177172522851846544827546752254039479}\cdot t^{23}+\frac{261567756972267595430364504113390202302167792060319371858439842308384210890625}{511177172522851846544827546752254039479}\cdot t^{21}-\frac{2218530802309070021024291906354660596501885354364875376551694632090496231906250}{511177172522851846544827546752254039479}\cdot t^{19}+\frac{14503136277338632222152035048984599922482415036399307940868990512953374522203125}{511177172522851846544827546752254039479}\cdot t^{17}-\frac{71596624054076912238141181726766470068875023092765683646996437707149368949375000}{511177172522851846544827546752254039479}\cdot t^{15}+\frac{260231886104716472977789104310904195217620818212022764565102776326036103089765625}{511177172522851846544827546752254039479}\cdot t^{13}-\frac{674480967849672146450791488331802896007644544275416385829605427010307112661468750}{511177172522851846544827546752254039479}\cdot t^{11}+\frac{1195121162964850220699971417571689444132233699107239286990483146642295248356703125}{511177172522851846544827546752254039479}\cdot t^9-\frac{1363378598545218451959271040799767112840851852825849596038175712766469285788937500}{511177172522851846544827546752254039479}\cdot t^7+\frac{909025020591112703069735275940144566896002107503670700138611240165627501661953125}{511177172522851846544827546752254039479}\cdot t^5-\frac{294687716555671314827868070204361083078732190606927515972559142556766158730156250}{511177172522851846544827546752254039479}\cdot t^3+\frac{29629035212755729957334471157149415749227676737539465019795262217994311734765625}{511177172522851846544827546752254039479}\cdot t$

Warning: This rule has negative weights!

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.