Difference between revisions of "H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0"
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(Created page with "==Theorem== If $n \geq 0$ is an integer, then $$\mathbf{H}_{-(n+\frac{1}{2})}(z) = (-1)^n J_{n+\frac{1}{2}}(z),$$ where $\mathbf{H}$ denotes a Struve function and $J$ deno...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=H (nu)(x) geq 0 for x gt 0 and nu geq 1/2|next= | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=H (nu)(x) geq 0 for x gt 0 and nu geq 1/2|next=H (1/2)(z)=sqrt(2/(pi z))(1-cos(z))}}: $12.1.15$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 01:05, 21 December 2017
Theorem
If $n \geq 0$ is an integer, then $$\mathbf{H}_{-(n+\frac{1}{2})}(z) = (-1)^n J_{n+\frac{1}{2}}(z),$$ where $\mathbf{H}$ denotes a Struve function and $J$ denotes Bessel J.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $12.1.15$
