Rule: Q[2, 48]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{50}-\frac{690785532487261846159174451762}{292195665583528468474853233}\cdot t^{48}+\frac{187725054971155862364498292114068}{292195665583528468474853233}\cdot t^{46}-\frac{1354864423356779130840820416234390}{12704159373196889933689271}\cdot t^{44}+\frac{307873555992668818018679211241538355}{25408318746393779867378542}\cdot t^{42}-\frac{50854392583343303788401456654315406395}{50816637492787559734757084}\cdot t^{40}+\frac{3165042323608687412409112953634464023835}{50816637492787559734757084}\cdot t^{38}-\frac{15986902540586031843881265045045969340545}{5349119736082901024711272}\cdot t^{36}+\frac{4801953131760735519984023910577578084858075}{42792957888663208197690176}\cdot t^{34}-\frac{284740659041764959570066341692527126577372275}{85585915777326416395380352}\cdot t^{32}+\frac{1674989351796753244712330196346121692364598825}{21396478944331604098845088}\cdot t^{30}-\frac{62663198057048656994478031570580019270729813825}{42792957888663208197690176}\cdot t^{28}+\frac{3722555392825401447545922065996221975452699196575}{171171831554652832790760704}\cdot t^{26}-\frac{87433232701418437610993203576147568421235503054375}{342343663109305665581521408}\cdot t^{24}+\frac{806339722881703841900049504237840219210656186773125}{342343663109305665581521408}\cdot t^{22}-\frac{11562898740681159501172756427666277865344661188958125}{684687326218611331163042816}\cdot t^{20}+\frac{1017275746153487584523051296556632553710295624652961875}{10954997219497781298608685056}\cdot t^{18}-\frac{8424685007480385147912216592364718391915635927194116875}{21909994438995562597217370112}\cdot t^{16}+\frac{12823147165965636725194952526199573000731018720852628125}{10954997219497781298608685056}\cdot t^{14}-\frac{55582573231818638765901500522438947194342489030038803125}{21909994438995562597217370112}\cdot t^{12}+\frac{328343535719008062386105675989064442742212968683665440625}{87639977755982250388869480448}\cdot t^{10}-\frac{621090188802885233394131675421496787146640378076588815625}{175279955511964500777738960896}\cdot t^8+\frac{342737237041388393793296210551362579901797342074296528125}{175279955511964500777738960896}\cdot t^6-\frac{189283867191127353539145942935543433664805862397138453125}{350559911023929001555477921792}\cdot t^4+\frac{155043449355262276343533487685415619567569979963213953125}{2804479288191432012443823374336}\cdot t^2-\frac{4832121260775887965916841297411512218813363901171578125}{5608958576382864024887646748672}$

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.