In case you don't already have all this, permit me to identify it as
a confluent hypergeometric function. Abramowitz and Stegun (1964)
Handbook of Mathematical Functions (National Bureau of Standard, Applied
Math Series 55, expression 13.2.5):
Gamma(a)U(a, b, z) =
integral{over t=0 to Inf of
exp(-z*t)*((t^(a-1))*((1+t)^(b-a-1))*dt}
See also Luke (1969) The Special Functions and their Approximations,
vol. I (Academic Press, p. 116, sec. 4.2, expr. (7)).
It is probably contained in any book that discusses the confluent
hypergeometric function.
I would write the chi-square as a gamma distribution, then factor out
the "c" in your expression, then change variables to get an integral of
this form.
Abramowitz and Stegun is available on the web. I felt the need to
download two different versions, because one was searchable but
incomplete while the other was complete but not searchable. See, e.g.,
"www.math.sfu.ca/~cbm/aands".
hope this helps,
Spencer Graves
MARK LEEDS wrote:
> i don't know it off the top of my head but there's a relation between powers
> of the chi squared and the gamma dsitribution.
> check it out in casella and berger or arnold.
>
>
> mark
>
>
> ----- Original Message -----
> From: "Philip He" <[EMAIL PROTECTED]>
> To: <[email protected]>
> Sent: Monday, May 15, 2006 2:52 PM
> Subject: [R] E(1/(X+c)) ? where X ~ Chi-square(n) and c is a constant.
>
>
>> Hi all,
>>
>> Can someone help me with the following expectation in a closed form?
>>
>> E(1/(X+c))
>>
>> where X ~ Chi-square(n) and c is a constant.
>>
>> Thanks.
>>
>> [[alternative HTML version deleted]]
>>
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