Difference between revisions of "Relationship between Scorer Hi and Airy functions"
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$\mathrm{Hi}(x)=\mathrm{Bi}(x)\displaystyle\int_{-\infty}^x \mathrm{Ai}(t) | + | $$\mathrm{Hi}(x)=\mathrm{Bi}(x)\displaystyle\int_{-\infty}^x \mathrm{Ai}(t) \mathrm{d}t - \mathrm{Ai}(x)\displaystyle\int_{-\infty}^x \mathrm{Bi}(t)\mathrm{d}t,$$ |
where $\mathrm{Hi}$ denotes the [[Scorer Hi]] function, $\mathrm{Ai}$ denotes the [[Airy Ai]] function, and $\mathrm{Bi}$ denotes the [[Airy Bi]] function. | where $\mathrm{Hi}$ denotes the [[Scorer Hi]] function, $\mathrm{Ai}$ denotes the [[Airy Ai]] function, and $\mathrm{Bi}$ denotes the [[Airy Bi]] function. | ||
Latest revision as of 15:28, 6 October 2016
Theorem
The following formula holds: $$\mathrm{Hi}(x)=\mathrm{Bi}(x)\displaystyle\int_{-\infty}^x \mathrm{Ai}(t) \mathrm{d}t - \mathrm{Ai}(x)\displaystyle\int_{-\infty}^x \mathrm{Bi}(t)\mathrm{d}t,$$ where $\mathrm{Hi}$ denotes the Scorer Hi function, $\mathrm{Ai}$ denotes the Airy Ai function, and $\mathrm{Bi}$ denotes the Airy Bi function.
