<p> Int(f,a,b,n) ... Simpson/Romberg Kernel </p>

8103c8d0-0e01-4f6f-b62e-e3020f899022 10 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

x α β Γ 1 α Gamma β α^* / x α 1 - (^* x β / - exp * :

L H N xd U 0 : dx H L - N / : 12 mat i 1 N range U i el L dx - (dx i * + eval : for U 31 line :

ε 1015 -^:

α 0.7352 :

β 245.4756 :

x α β Γ

ε α β Γ 131.67

L ε : H 10 : N 1000 : 13 mat

U L H N xd :

data Σ Finite diff's Cumul Integration vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

data j 1 U rows range Y j el U j el α β Γ eval : for U Y augment 21 line :

sub data 2 data rows 12 submatrix :

X 30.4 63.9 387.1 330 187.3 495.9 18 163.3 128.8 91 mat :

sub Σ sub

α 0.7352 :

β 245.4756 :

ε 1012 -^:

eval(,) drops timing ~ 0.75
acc acuuracy 50/100 plentty.
Smath Gamma(x) ... 4 decimals x α β CDF 1 α Gamma β α^* / t α 1 -^t β / - exp * t ε x int eval * :

CDF X α β CDF vectorize :

CDF 1.292 2.612 14.4915 12.4421 7.2545 18.3727 0.7877 6.3677 5.0819 91 mat

Excel 0.2233 0.3647 0.8684 0.8291 0.6644 0.9194 0.1551 0.6224 0.5508 91 mat :

<p> Int(f,a,b,n) ... Simpson/Romberg Kernel </p>

Simpson Integrator in the Romberg Transform Domain [0,1] <= [a,b] ...  
... integrates  Smath ainterp(X,Y,x), cinterp(X,Y,x), cubic(x) from  l_p_c_spline f a b n Int w s b a - (34 / 2 w * 1 - (* 14 / 2 w * 1 - (3^* - 12 / + (* a + : w G w s f 12 w * 1 - (2^- (* : α 0 : β 1 : h β α - n / : 14 mat Simpson 13 / h 2 / α G β G + (* h α k h * + G k 1 n 1 - sum * + (* 23 / h * α h 2 / - k h * + G k 1 n sum * + eval : 32 / b a - (* Simpson * 41 line :

t0 1 time :

x f x α β Γ :

n 100 :

f ε X n Int vectorize 0.2232 0.3646 0.8682 0.8289 0.6643 0.9192 0.1551 0.6223 0.5507 91 mat

Excel 0.2233 0.3647 0.8684 0.8291 0.6644 0.9194 0.1551 0.6224 0.5508 91 mat

1 time t0 - 9 s *