Difference between revisions of "Relationship between Scorer Gi and Airy functions"
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| − | + | ==Theorem== | |
The following formula holds: | The following formula holds: | ||
$$\mathrm{Gi}(x)=\mathrm{Bi}(x)\displaystyle\int_x^{\infty} \mathrm{Ai}(t)dt + \mathrm{Ai}(x)\displaystyle\int_0^x \mathrm{Bi}(t)dt,$$ | $$\mathrm{Gi}(x)=\mathrm{Bi}(x)\displaystyle\int_x^{\infty} \mathrm{Ai}(t)dt + \mathrm{Ai}(x)\displaystyle\int_0^x \mathrm{Bi}(t)dt,$$ | ||
where $\mathrm{Gi}$ denotes the [[Scorer Gi]] function, $\mathrm{Ai}$ denotes the [[Airy Ai]] function, and $\mathrm{Bi}$ denotes the [[Airy Bi]] function. | where $\mathrm{Gi}$ denotes the [[Scorer Gi]] function, $\mathrm{Ai}$ denotes the [[Airy Ai]] function, and $\mathrm{Bi}$ denotes the [[Airy Bi]] function. | ||
| − | === | + | ==Proof== |
| + | |||
| + | ==References== | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
Revision as of 22:27, 9 June 2016
Theorem
The following formula holds: $$\mathrm{Gi}(x)=\mathrm{Bi}(x)\displaystyle\int_x^{\infty} \mathrm{Ai}(t)dt + \mathrm{Ai}(x)\displaystyle\int_0^x \mathrm{Bi}(t)dt,$$ where $\mathrm{Gi}$ denotes the Scorer Gi function, $\mathrm{Ai}$ denotes the Airy Ai function, and $\mathrm{Bi}$ denotes the Airy Bi function.
