How to calculate the coefficient related to the expression of the krawtchouk moments

Hello I need to calculate this term

using this formulate

Where 2F1 in matlab is the hypergeometric function

Any answer can help me I'm stack with this problem 2 weeks please help

[Torsten]

It's very unusual that 1/p instead of x is the independent variable in the hypergeometric function. Are you sure your notation of 2F1 is the usual MATLAB notation used under

http://de.mathworks.com/help/symbolic/hypergeom.html#bt1nkmw-2

?

Best wishes

Torsten.

[jenny jenny]

Thanks Torsen for your comment Yes I'm sure It's the hypergemetric function and I need to calculate ak,n,p like I mentionned in the comment :

http://www.mathworks.com/matlabcentral/answers/275117#comment_352800

[Torsten]

syms n, N, p, x
taylor(hypergeom([-n, -x], [-N], 1/p),x)

See for example

http://www.wolframalpha.com/input/?i=taylor+series+hypergeometric2F1(-4,-x,-N,1%2Fp)

Best wishes

Torsten.

[jenny jenny]

Thank you so mutch Toresten But I don't understand how can that help me to calculate

[Torsten]

The a_k,n,p are the coefficients in front of the powers of x in the Taylor series representation you get from the taylor() command.

Best wishes

Torsten.

[jenny jenny]

thank you Torsten for my case I have

1. N=20 p=0.5 n=0
2. N=20 p=0.5 n=1
3. N=20 p=0.5 n=2
4. N=20 p=0.5 n=3

For the value of x I 're now what value I affected to x :(

[Torsten]

You got it ?

If you enter

http://www.wolframalpha.com/input/?i=Series%5Bhypergeometric2F1(-3,-x,-20,1%2F0.5),%7Bx,0,4%7D%5D

the result is

a_0,3,0.5,20 = 1
a_1,3,0.5,20 = -0.333918
a_2,3,0.5,20 = 0.0350877
a_3,3,0.5,20 = -0.00116959

I hope you receive the same results in MATLAB, too, using the taylor() command.

Best wishes

Torsten.

[jenny jenny]

I have an erreor </matlabcentral/answers/uploaded_files/48359/f.PNG>

[Torsten]

I can't see your uploaded file. Better attach it here using the "Attach File" button.

Best wishes

Torsten.

[jenny jenny]

I have an erreor

[Torsten]

But I already gave you the correct code:

syms x
taylor(hypergeom([-3, -x], [-20], 2),x)

Best wishes

Torsten.

[jenny jenny]

[Torsten]

Then I don't see another way as to copy the results from MATHEMATICA.

Best wishes

Torsten.

[jenny jenny]

Thanks a lot Toreson I think this is the correct answer But I have this warning in matlab I don't understand why but I'm appricate your time and your answer thank you so mutch

Answer 1

[Walter Roberson]

hypergeom([-n, -x], [-N], 1/p)

Just like when you asked before; see http://www.mathworks.com/matlabcentral/answers/274492-calculate-the-krawtchouk-moments-invariants#comment_351830

[jenny jenny]

thanks for your answer But what I need is to calculate

where

1) n=0 and (k=0 k=1 k=2 k=3)

2) n=1 and (k=0 k=1 k=2 k=3)

3) n=2 and (k=0 k=1 k=2 k=3)

4) n=3 and (k=0 k=1 k=2 k=3)

and p=0.5

my problem is about how to determinate the value of

using

[Walter Roberson]

Insufficient information about your notation. How is "a subscript k comma n comma p" defined?

On the left hand side you have a finite series of low order. On the right hand side you have something that is defined by an infinite summation. Clearly they cannot be defined by the taylor expansion of hypergeometric, as that would be a finite series that could at best approximate the hypergeometric.

[jenny jenny]

thank you so much for your answer I well use ak,n,p to calculate an other term all I have is this information (eaglity with the hypergeom) in the article they say that I use this egality to calculate ak,n,p please help :'( :'( what about the comment of Torsten

http://www.mathworks.com/matlabcentral/answers/275117#comment_352814

[jenny jenny]

hello every body in a book of informatique I have find this information it's correcte

were

[Walter Roberson]

What does (-k) subscript n mean here?