Böhmer integral - Böhmer integral

Yilda matematika, a Böhmer integral bu ajralmas tomonidan kiritilgan Bömer (1939) umumlashtiruvchi The Frenel integrallari.

Tomonidan berilgan ikkita versiya mavjud

${ displaystyle displaystyle C (x, alpha) = int _ {x} ^ { infty} t ^ { alfa -1} cos (t) , dt}$

${ Displaystyle displaystyle S (x, alfa) = int _ {x} ^ { infty} t ^ { alfa -1} sin (t) , dt}$

Binobarin, Frenel integrallarini Bohmer integrallari sifatida quyidagicha ifodalash mumkin

${ displaystyle operator nomi {S} (y) = { frac {1} {2}} - { frac {1} { sqrt {2 pi}}} cdot operator nomi {S} chap ({ frac {1} {2}}, y ^ {2} o'ng)}$

${ displaystyle operator nomi {C} (y) = { frac {1} {2}} - { frac {1} { sqrt {2 pi}}} cdot operator nomi {C} chap ({ frac {1} {2}}, y ^ {2} o'ng)}$

The sinus integral va kosinus integrali Bömer integrallari bilan ham ifodalanishi mumkin

${ displaystyle operator nomi {Si} (x) = { frac { pi} {2}} - operator nomi {S} (x, 0)}$

${ displaystyle operator nomi {Ci} (x) = { frac { pi} {2}} - operator nomi {C} (x, 0)}$

Adabiyotlar

• Böhmer, Pol Evgen (1939). Differenzengleichungen und bestimmte Integrale (nemis tilida). Leypsig, K. F. Koehler Verlag.
• Oldxem, Keyt B.; Myland, Jan; Ispaniya, Jerom (2010). Funksiyalar atlasi. Springer Science & Business Media. p. 401.

Bu matematik tahlil - tegishli maqola a naycha. Siz Vikipediyaga yordam berishingiz mumkin uni kengaytirish.