Difference between revisions of "Integral of Bessel J for Re(nu) greater than -1"
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(Created page with "==Theorem== The following formula holds for $\mathrm{Re}(\nu)>-1$: $$\displaystyle\int_0^z J_{\nu}(t) \mathrm{d}t = 2 \displaystyle\sum_{k=0}^{\infty} J_{\nu+2k+1}(z),$$ where...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Integral of monomial times Bessel J|next=}}: $11.1.2$ | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Integral of monomial times Bessel J|next=Integral of Bessel J for nu=2n}}: $11.1.2$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 16:56, 27 June 2016
Theorem
The following formula holds for $\mathrm{Re}(\nu)>-1$: $$\displaystyle\int_0^z J_{\nu}(t) \mathrm{d}t = 2 \displaystyle\sum_{k=0}^{\infty} J_{\nu+2k+1}(z),$$ where $J_{\nu}$ denotes the Bessel function of the first kind.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $11.1.2$
