## 520 Reputation

9 years, 173 days

## Social Networks and Content at Maplesoft.com

Seldom to ask question after retired math hobby Just waiting for beauty who born in 1994 And waited for her email to mavio@protonmail.com What is the difference in ownership among different universe?

## i think this because chapter 3 page 86 ...

i think this because chapter 3 page 86

3.2.1 said  z-transform of this network can be written as

rational function (3.1)

## i think this because chapter 3 page 86 ...

i think this because chapter 3 page 86

3.2.1 said  z-transform of this network can be written as

rational function (3.1)

## the general case result (2) still has zt...

the general case result (2) still has ztrans, it should be a simple rational function

## the general case result (2) still has zt...

the general case result (2) still has ztrans, it should be a simple rational function

## if it is impossible, how arthur derive t...

if it is impossible, how Author derive this? need transformation?

i see that they are quite similar, like just need a few more steps, then success

can it be manually done by observation using below script

restart;
n := 1:
rodrigues := exp(x)*(x^alpha)/n!*diff(exp(-x)*(x^(n+alpha)), x\$n):
rodrigues := subs(x=2*p, rodrigues):
rodrigues := subs(alpha=1/2, rodrigues):
rodrigues1 := factor(simplify(rodrigues));
n := 2:
rodrigues := exp(x)*(x^alpha)/n!*diff(exp(-x)*(x^(n+alpha)), x\$n):
rodrigues := subs(x=2*p, rodrigues):
rodrigues := subs(alpha=1/2, rodrigues):
rodrigues2 := factor(simplify(rodrigues));
n := 3:
rodrigues := exp(x)*(x^alpha)/n!*diff(exp(-x)*(x^(n+alpha)), x\$n):
rodrigues := subs(x=2*p, rodrigues):
rodrigues := subs(alpha=1/2, rodrigues):
rodrigues3 := factor(simplify(rodrigues));

-(4 p - 3) p
1   /    2            \
- p \16 p  - 40 p + 15/
4
1    /    3        2              \
- -- p \64 p  - 336 p  + 420 p - 105/
24

## if it is impossible, how arthur derive t...

if it is impossible, how Author derive this? need transformation?

i see that they are quite similar, like just need a few more steps, then success

can it be manually done by observation using below script

restart;
n := 1:
rodrigues := exp(x)*(x^alpha)/n!*diff(exp(-x)*(x^(n+alpha)), x\$n):
rodrigues := subs(x=2*p, rodrigues):
rodrigues := subs(alpha=1/2, rodrigues):
rodrigues1 := factor(simplify(rodrigues));
n := 2:
rodrigues := exp(x)*(x^alpha)/n!*diff(exp(-x)*(x^(n+alpha)), x\$n):
rodrigues := subs(x=2*p, rodrigues):
rodrigues := subs(alpha=1/2, rodrigues):
rodrigues2 := factor(simplify(rodrigues));
n := 3:
rodrigues := exp(x)*(x^alpha)/n!*diff(exp(-x)*(x^(n+alpha)), x\$n):
rodrigues := subs(x=2*p, rodrigues):
rodrigues := subs(alpha=1/2, rodrigues):
rodrigues3 := factor(simplify(rodrigues));

-(4 p - 3) p
1   /    2            \
- p \16 p  - 40 p + 15/
4
1    /    3        2              \
- -- p \64 p  - 336 p  + 420 p - 105/
24

## After adding assuming X > 1, it can n...

After adding assuming X > 1, it can not evaluate too
, how to define a range for it to transform successfully?

Bernoulli
charc := 1/(I*X/(-1+exp(I*X)))^n;
Density := int(exp(-I*X*u)/(I*X/(-1+exp(I*X)))^n, X = -infinity .. infinity) assuming X > 1;

Density := int(exp(-I*X*u)/(I*X/(-1+exp(I*X)))^n, X = 1.1 .. infinity)

can not evaluate

## WoW!!!!  it success to evaluate wh...

WoW!!!!  it success to evaluate

why not set pdf at the same time?

## WoW!!!!  it success to evaluate wh...

WoW!!!!  it success to evaluate

why not set pdf at the same time?

## after using Unapply RealDist := Distrib...

after using Unapply

RealDist := Distribution(Dist(t-1));
Error, (in Statistics:-Distribution) invalid input: IsKnownDistribution expects its 1st argument, dn, to be of type name, but received Unapply(Pi*erf(t), t)

after using unapply

unexpected argument

## after using Unapply RealDist := Distrib...

after using Unapply

RealDist := Distribution(Dist(t-1));
Error, (in Statistics:-Distribution) invalid input: IsKnownDistribution expects its 1st argument, dn, to be of type name, but received Unapply(Pi*erf(t), t)

after using unapply

unexpected argument

## sorry for misunderstanding, just conside...

sorry for misunderstanding, just consider all i in small letter or all in big letter

## sorry for misunderstanding, just conside...

sorry for misunderstanding, just consider all i in small letter or all in big letter

## yes, by madan's result, in other words t...

yes, by madan's result, in other words to see how integration of two things result in new distribution

i just want to produce madan's answer not only using gamma, i want to use all different kinds of distributions to do madan's result.

in the link of handbook of distribution's derivation of gamma, told the method

to find gamma that means using other process or your own generating function, you can also using the method and

then integrate with normal distribution, to find madan's result.

i want to investigate how these processes change the tail of normal distribution.

of course, furthermore not only normal distribution.

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