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mathematical physics > special function > Scorer's function

mathematical analysis > functional analysis > special function > Scorer's function

Preferred term

Scorer's function

In mathematics, the Scorer's functions are special functions studied by Scorer (1950) and denoted Gi(x) and Hi(x).
Hi(x) and -Gi(x) solve the equation

${\\displaystyle y''(x)-x\\ y(x)={\ rac {1}{\\pi }}}$

and are given by

${\\displaystyle \\mathrm {Gi} (x)={\ rac {1}{\\pi }}\\int _{0}^{\\infty }\\sin \\left({\ rac {t^{3}}{3}}+xt\ ight)\\,dt,}$

${\\displaystyle \\mathrm {Hi} (x)={\ rac {1}{\\pi }}\\int _{0}^{\\infty }\\exp \\left(-{\ rac {t^{3}}{3}}+xt\ ight)\\,dt.}$

special function

fonction de Scorer

French

URI

http://data.loterre.fr/ark:/67375/PSR-Q7FKCBLQ-N

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