gsl-shell.git - gsl-shell

diff --git a/examples/hermite.lua b/examples/hermite.lua
index 99a6754a..b5cb25f1 100644
--- a/examples/hermite.lua
+++ b/examples/hermite.lua

@@ -1,31 +1,28 @@

-function hermiteLp(n,x)

- return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * (-4)^(n/2) * fact(n/2) * laguerre(n/2, -1/2, x^2)

-end

-

-p = plot()

-p:addline(fxline(|x| hermiteLp(4, x), -12, 12), 'darkgreen')

-p:addline(fxline(|x| hermiteLp(2, x), -12, 12), 'blue')

-p:addline(fxline(|x| hermiteLp(50, x), -12, 12, 1024), 'magenta')

-p:show()

-

-function hermiteU(n,x)

- return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * 2^n * hypergU((1-n)/2, 3/2, x^2)

-end

-

-function hermiteFp(n,x)

- return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * (-1)^(n/2) * fact(n)/fact(n/2) * hyperg1F1(-n/2, 1/2, x^2)

-end

-

-

-p2 = plot()

-p2:addline(fxline(|x| hermiteFp(4, x), -12, 12), 'darkgreen')

-p2:addline(fxline(|x| hermiteFp(2, x), -12, 12), 'blue')

-p2:addline(fxline(|x| hermiteFp(50, x), -12, 12, 1024), 'magenta')

-p:show()

-

-

--- p3 = plot()

--- p3:add_line(fxline(|x| hermiteU(4, x), -12, 12), 'darkgreen')

--- p3:add_line(fxline(|x| hermiteU(2, x), -12, 12), 'blue')

--- p3:add_line(fxline(|x| hermiteU(50, x), -12, 12, 1024), 'magenta')

+

+local function hermiteLp(n,x)

+ return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * (-4)^(n/2) * fact(n/2) * laguerre(n/2, -1/2, x^2)

+end

+

+local function hermiteU(n,x)

+ return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * 2^n * hypergU((1-n)/2, 3/2, x^2)

+end

+

+local function hermiteFp(n,x)

+ return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * (-1)^(n/2) * fact(n)/fact(n/2) * hyperg1F1(-n/2, 1/2, x^2)

+end

+

+local function demo_gen(hermiteFF)

+ local p = plot('Hermite functions')

+ p:addline(fxline(|x| hermiteFF(2, x), -10, 10), 'red')

+ p:addline(fxline(|x| hermiteFF(4, x), -10, 10), 'blue', {{'dash', 7, 3}})

+ p:addline(fxline(|x| hermiteFF(16, x), -10, 10, 512), 'green')

+ p:show()

+end

+

+demo1 = || demo_gen(hermiteLp)

+demo2 = || demo_gen(hermiteFp)

+demo3 = || demo_gen(hermiteU)

+

+print 'demo1() - hermite function using Laguerre polynomials'

+print 'demo2() - hermite function using Hypergeometric 1F1 function'

+print 'demo3() - hermite function using Hypergeometric U function (broken)'