Rule: Q[4, 45]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{49}-\frac{1537941489400837442117679296021997144}{177036531294596661352651300338773}\cdot t^{47}+\frac{15683929370310663266474903400854997806856}{7258497783078463115458703313889693}\cdot t^{45}-\frac{2373405748325946181313829135848806992519390}{7258497783078463115458703313889693}\cdot t^{43}+\frac{34965454477640133000074576736527867030969970}{1036928254725494730779814759127099}\cdot t^{41}-\frac{127247659754142243730128142495189565478602655}{50581866084170474672186085811078}\cdot t^{39}+\frac{7116205621387214994851294254910534685293059515}{50581866084170474672186085811078}\cdot t^{37}-\frac{1220198608672994909977428334590228588078095557515}{202327464336681898688744343244312}\cdot t^{35}+\frac{81324391553517566590936800966531494909763308536725}{404654928673363797377488686488624}\cdot t^{33}-\frac{2124568164607482607162736332145284812340596454353225}{404654928673363797377488686488624}\cdot t^{31}+\frac{43691973539551796169511744876281284419907172960499575}{404654928673363797377488686488624}\cdot t^{29}-\frac{2830966114140668649459096205578035482497079636479552525}{1618619714693455189509954745954496}\cdot t^{27}+\frac{36027965030209895797157375308669328449766833984688499975}{1618619714693455189509954745954496}\cdot t^{25}-\frac{1432832966134547034008533448589930869499692703907087404375}{6474478858773820758039818983817984}\cdot t^{23}+\frac{11031826093249543929902840193042562739380098315333601929375}{6474478858773820758039818983817984}\cdot t^{21}-\frac{259848946812676043761553194263202667748015757674521244931875}{25897915435095283032159275935271936}\cdot t^{19}+\frac{4603751540668158721607946838813222071680194616838732863998125}{103591661740381132128637103741087744}\cdot t^{17}-\frac{30007910595611815205288734318782151561744497850917476123750625}{207183323480762264257274207482175488}\cdot t^{15}+\frac{69906272087654449359794802211190611686973592156984086512721875}{207183323480762264257274207482175488}\cdot t^{13}-\frac{448052262212855383779882714893668301507279472013641326525653125}{828733293923049057029096829928701952}\cdot t^{11}+\frac{468689948889818127817321945530430425309574922843690805022790625}{828733293923049057029096829928701952}\cdot t^9-\frac{1189917545610040054649328395141714403404856090350855364239971875}{3314933175692196228116387319714807808}\cdot t^7+\frac{411021599370556609740330396223368122655873138345844667914434375}{3314933175692196228116387319714807808}\cdot t^5-\frac{3261050198515998960740257038511926601880901339443975128640625}{167844717756566897626146193403281408}\cdot t^3+\frac{24309741925743407605982199737485515009888509581513105291546875}{26519465405537569824931098557718462464}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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