Rule: Q[16, 25]

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.

• $P_1$:
  $65536\cdot t^{16}-3932160\cdot t^{14}+89456640\cdot t^{12}-984023040\cdot t^{10}+5535129600\cdot t^8-15498362880\cdot t^6+19372953600\cdot t^4-8302694400\cdot t^2+518918400$
• $P_2$:
  $65536\cdot t^{41}-\frac{8128264707899392}{408408193}\cdot t^{39}+\frac{3316304343627431936}{1225224579}\cdot t^{37}-\frac{89265775658405232640}{408408193}\cdot t^{35}+\frac{4785466924215639101440}{408408193}\cdot t^{33}-\frac{180428931744118839541760}{408408193}\cdot t^{31}+\frac{4945799066484492884828160}{408408193}\cdot t^{29}-\frac{100508620350367918459330560}{408408193}\cdot t^{27}+\frac{1530713918426998939541107200}{408408193}\cdot t^{25}-\frac{17548070673308021668838016000}{408408193}\cdot t^{23}+\frac{151307080232050296066056544000}{408408193}\cdot t^{21}-\frac{975744398087960610449340000000}{408408193}\cdot t^{19}+\frac{4656342434289480731694037140000}{408408193}\cdot t^{17}-\frac{16176787556428454777457395760000}{408408193}\cdot t^{15}+\frac{39965499815413888429420887180000}{408408193}\cdot t^{13}-\frac{67925523938009488715300115780000}{408408193}\cdot t^{11}+\frac{75753940895289273032147104498125}{408408193}\cdot t^9-\frac{51699180204188815459145072838750}{408408193}\cdot t^7+\frac{38672513977790445771516976603125}{816816386}\cdot t^5-\frac{6501999614867367465850711340625}{816816386}\cdot t^3+\frac{2470336694583616570015044365625}{6534531088}\cdot t$

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.