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Scorer's function : ウィキペディア英語版
Scorer's function

In mathematics, the Scorer's functions are special functions studied by and denoted Gi(''x'') and Hi(''x'').
They solve the equation
:y''(x) - x\ y(x) = \frac
and are given by
:\mathrm(x) = \frac \int_0^\infty \sin\left(\frac + xt\right)\, dt,
:\mathrm(x) = \frac \int_0^\infty \exp\left(-\frac + xt\right)\, dt.
The Scorer's functions can also be defined in terms of Airy functions:
:\begin
\mathrm(x) &(t) \, dt + \mathrm(x) \int_0^x \mathrm(t) \, dt, \\
\mathrm(x) &^x \mathrm(t) \, dt - \mathrm(x) \int_^x \mathrm(t) \, dt. \end

==References==

*
*f(x)e^dx and the tabulation of the function (z)=\frac\int^\infty_0\left(uz+\frac 13 u^3\right)du | doi=10.1093/qjmam/3.1.107 | mr=0037604 |id=| year=1950 | journal=The Quarterly Journal of Mechanics and Applied Mathematics | issn=0033-5614 | volume=3 | pages=107–112}}

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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