Re: 1F1 with matrix argument

"A" == A N Niel <anniel@xxxxxxxxxxxxxxxxxxxxx> writes:

>> > I have come across the problem of differentiating the
>> Hypergeometric > function 1F1(a, b; D), where 'D' is a diagonal
>> matrix. Essentially, I > need to compute
>> >
>> > \partial 1F1(a, b; D) > -------------------------- > \partial
>> d_{ii}
>> >
>> > The most amenable avenue so far seems to be the 'zonal-polynomial'
>> based > representation of 1F1, but before I dive in, I wanted to know
>> if there > are certain standard known results about this function.

A> 1F1(a,b;D), where D is a diagonal matrix: the result is again a
A> diagonal matrix, where you apply 1F1(a,b;.) to each of the diagonal
A> entries.

This last claim uses a definition of 1F1 that i don't want, in these sense
that 1F1(a, b; D) is a scalar function of the matrix D, not a matrix
function. Hence I can't just apply 1F1 to the diagonal elements.

-suvrit
.

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