Difference between revisions of "H (nu)(x) geq 0 for x gt 0 and nu geq 1/2"
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(Created page with "==Theorem== The following formula holds for $x>0$ and $\nu \geq \dfrac{1}{2}$: $$\mathbf{H}_{\nu}(x) \geq 0,$$ where $\mathbf{H}$ denotes a Struve function. ==Proof== ==...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1)|next=}}: $12.1.14$ | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1)|next=H_(-(n+1/2))(z)=(-1)^n J_(n+1/2)(z) for integer n geq 0}}: $12.1.14$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 00:57, 21 December 2017
Theorem
The following formula holds for $x>0$ and $\nu \geq \dfrac{1}{2}$: $$\mathbf{H}_{\nu}(x) \geq 0,$$ where $\mathbf{H}$ denotes a Struve function.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $12.1.14$
