Rule: Q[16, 32]

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.

• $P_1$:
  $65536\cdot t^{16}-3932160\cdot t^{14}+89456640\cdot t^{12}-984023040\cdot t^{10}+5535129600\cdot t^8-15498362880\cdot t^6+19372953600\cdot t^4-8302694400\cdot t^2+518918400$
• $P_2$:
  $65536\cdot t^{48}-\frac{69351526698614895189700116480}{2470287875140857532409}\cdot t^{46}+\frac{6483185255520628227237179228160}{1181442027241279689413}\cdot t^{44}-\frac{17662822601656699941361305705185280}{27173166626549432856499}\cdot t^{42}+\frac{1420244368106473317464713136643072000}{27173166626549432856499}\cdot t^{40}-\frac{1563650765524392407208083095366544506880}{516290165904439224273481}\cdot t^{38}+\frac{202969632141131744148562432035199043276800}{1548870497713317672820443}\cdot t^{36}-\frac{3454122774320349256251509404548973685657600}{797902983670496982968107}\cdot t^{34}+\frac{88339641292219214697462130449819677967545600}{797902983670496982968107}\cdot t^{32}-\frac{1763411648570029685292355538255992706944768000}{797902983670496982968107}\cdot t^{30}+\frac{27577023283679261874215390909748113113065024000}{797902983670496982968107}\cdot t^{28}-\frac{337868655081114150854293389303367895624777664000}{797902983670496982968107}\cdot t^{26}+\frac{3232239741460749275738330658817462235177833800000}{797902983670496982968107}\cdot t^{24}-\frac{1042761209438200118575380869103489825038924400000}{34691434072630303607309}\cdot t^{22}+\frac{312635386213526636900982017302249037095398900000}{1825864951191068610911}\cdot t^{20}-\frac{1347710364467770967700387210114162986700023220000}{1825864951191068610911}\cdot t^{18}+\frac{253633513829700057253880103242555977660940690625}{107403820658298153583}\cdot t^{16}-\frac{586709753912358247347629285570667427295680837500}{107403820658298153583}\cdot t^{14}+\frac{86103829287858517805692188806518089238218384375}{9763983696208923053}\cdot t^{12}-\frac{92335083664388684028910287842094739176658078125}{9763983696208923053}\cdot t^{10}+\frac{489728184462960143062880821019062779702592903125}{78111869569671384424}\cdot t^8-\frac{89731446433781977746279189093543480145533234375}{39055934784835692212}\cdot t^6+\frac{59942355998203488673427868777948049855725046875}{156223739139342768848}\cdot t^4-\frac{3106050752730552990557866526974678670948484375}{156223739139342768848}\cdot t^2+\frac{315906529272927452123758867790612666173828125}{2499579826229484301568}$

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.