Re: plotting integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg131687] Re: plotting integrals
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 21 Sep 2013 04:35:50 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-outx@smc.vnet.net
• Delivered-to: mathgroup-newsendx@smc.vnet.net
• References: <20130920110737.A26746A58@smc.vnet.net>

```The definitions of Subscript[F,TPT] and Subscript[=E7,B] should not have th=
e
argument, x, since it is the variable of integration in the definition of
Subscript[F,TPT]. And presumably you want to plot with varying values of a.
Also, functions which use numerical techniques should have their arguments
restricted to numerical values.

=F8[x_, =F9_] := (=F9/=F0)^(1/4) Exp[-1/2 =F9 x^2];

=F81[x_, a_, n_] :=
Sqrt[(2 n)!!/((2 n - 1)!! =F0)] Cos[a*x]^n;

Subscript[F, TPT][a_?NumericQ, n_?NumericQ] :=
NIntegrate[
=F81[x, a, n]*=F8[x, a*Sqrt[2 n (n - 1)]],
{x, -=F0/2, =F0/2}];

Subscript[=E7, B][a_?NumericQ, n_?NumericQ] :=
Sqrt[(1 - Subscript[F, TPT][a, n])];

Plot[Subscript[=E7, B][a, 3],
{a, -.1, 2 Pi},
Frame -> True,
Axes -> False,
Exclusions -> 0]

Plot[Subscript[=E7, B][a, 3],
{a, 0, .01},
Frame -> True, Axes -> False,
Exclusions -> 0]

Bob Hanlon

On Fri, Sep 20, 2013 at 7:07 AM, Herman <btta2010 at gmail.com> wrote:

> Dear All,
>
> I would like to plot the function Subscript[\[Eta], B] but I got errors.
>
>
> \[Psi][x_, \[Omega]_] := (\[Omega]/\[Pi])^(1/4)
>   Exp[-1/2 \[Omega] x^2]
>
> \[Psi]1[x_, a_, n_] := Sqrt[(2 n)!!/((2 n - 1)!! \[Pi])] Cos [a*x]^n
>
> Subscript[F, TPT][x_, a_, n_] :=
>  NIntegrate[\[Psi]1[x, a, n]*\[Psi][x,
>     a*Sqrt[2 n (n - 1)]], {x, -\[Pi]/2, \[Pi]/2}]
>
> Subscript[\[Eta], B][x_, a_,
>   n_] := Sqrt[(1 - Subscript[F, TPT][x, a, n])]
>
> Plot[Subscript[\[Eta], B][x, 1, 3], {x, -\[Pi]/2, \[Pi]/2}]
>
>

```

• Prev by Date: Re: Extract columns based on their the title in header
• Next by Date: Import CSV can not understand string correctly
• Previous by thread: plotting integrals
• Next by thread: Re: plotting integrals