Difference between revisions of "Integral of Bessel J for nu=n+1"
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(Created page with "==Theorem== The following formula holds for $n>0$: $$\displaystyle\int_0^z J_{n+1}(t) \mathrm{d}t = \displaystyle\int_0^z J_{n-1}(t) \mathrm{d}t - 2J_n(z),$$ where $J_{n+1}$ d...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Integral of Bessel J for nu=2n+1|next=}}: $11.1.5$ | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Integral of Bessel J for nu=2n+1|next=Integral of Bessel J for nu=1}}: $11.1.5$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 17:01, 27 June 2016
Theorem
The following formula holds for $n>0$: $$\displaystyle\int_0^z J_{n+1}(t) \mathrm{d}t = \displaystyle\int_0^z J_{n-1}(t) \mathrm{d}t - 2J_n(z),$$ where $J_{n+1}$ denotes the Bessel function of the first kind.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $11.1.5$
