- #1

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Is there somebody who can help me how to solve this integral

[tex]

\int_{0}^{+\infty} dr r^{^{n+1}} e^{-\alpha r} j_l(kr)

[/tex]

[tex]

\int_{0}^{+\infty} dr r^{^{n+1}} e^{-\alpha r} j_l(kr)

[/tex]

Last edited:

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- Thread starter hmhm696
- Start date

- #1

- 3

- 0

[tex]

\int_{0}^{+\infty} dr r^{^{n+1}} e^{-\alpha r} j_l(kr)

[/tex]

Last edited:

- #2

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- #3

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- 5

If[Re[a] >

0 && (Abs[Im[k]] <

Re[a] || (Abs[Im[k]] == Re[a] && Re[n] < 0)) && (Re[k] >

0 || (Im[k] > 0 && Re[k] == 0)),

2^(-1 - l) a^(-2 - n) (k^2/a^2)^(l/2) Sqrt[\[Pi]]

Gamma[2 + l + n] Hypergeometric2F1Regularized[1/2 (2 + l + n),

1/2 (3 + l + n), 3/2 + l, -(k^2/a^2)],

Integrate[

E^(-a r) r^(1 + n) SphericalBesselJ[l, k r], {r, 0, \[Infinity]},

Assumptions ->

Abs[Im[k]] > Re[a] || (Abs[Im[k]] >= Re[a] && Re[n] >= 0) ||

Re[k] < 0 || (Re[k] <= 0 && Im[k] <= 0) || Re[a] <= 0]]

- #4

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http://functions.wolfram.com/Bessel-TypeFunctions/SphericalBesselJ/02/

and then use formula attached below which is taken from G & R

- #5

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I think that given formula has error in the part where it derivative by alpha instead of betha.

For me is important a process, how i can get it.

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