Difference between revisions of "Relationship between Scorer Gi and Airy functions"
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− | + | ===Theorem=== | |
− | + | The following formula holds: | |
$$\mathrm{Gi}(x)=\mathrm{Bi}(x)\displaystyle\int_x^{\infty} \mathrm{Ai}(t)dt + \mathrm{Ai}(x)\displaystyle\int_0^x \mathrm{Bi}(t)dt,$$ | $$\mathrm{Gi}(x)=\mathrm{Bi}(x)\displaystyle\int_x^{\infty} \mathrm{Ai}(t)dt + \mathrm{Ai}(x)\displaystyle\int_0^x \mathrm{Bi}(t)dt,$$ | ||
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=== | |
− | + | ||
− | + | [[Category:Theorem]] |
Revision as of 08:03, 5 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.