تكامل أسي

في الرياضيات، التكامل الأسي (بالإنجليزية: Exponential integral)‏ يشار لها بـ $\operatorname {Ei}$ ، هي دالة خاصة في المستوى العقدي.^[1]^[2]^[3] هي معرفة كتكامل محدد للنسبة بين الدالة الأسية و عمدتها.

تعاريف

لكل عدد حقيقي غير منعدم $x$ ، التكامل الأسي $\operatorname {Ei}$ معرف كالتالي:

\displaystyle \operatorname {Ei} (x)=-\int _{-x}^{\infty }{\dfrac {e^{-t}}{t}}\mathrm {d} t.

بالنسبة للأعداد العقدية هي معرفة كـ:

\mathrm {E} _{1}(z)=\int _{z}^{\infty }{\frac {e^{-t}}{t}}\,dt,\qquad |{\rm {Arg}}(z)|<\pi

انظر أيضا

دالة التكامل اللوغاريتمي

مراجع

^ Tseng، Peng-Hsiang؛ Lee، Tien-Chang (26 فبراير 1998). "Numerical evaluation of exponential integral: Theis well function approximation". Journal of Hydrology. ج. 205 ع. 1–2: 38–51. Bibcode:1998JHyd..205...38T. DOI:10.1016/S0022-1694(97)00134-0. مؤرشف من الأصل في 2011-08-27.
^ Giao، Pham Huy (1 مايو 2003). "Revisit of Well Function Approximation and An Easy Graphical Curve Matching Technique for Theis' Solution". Ground Water. ج. 41 ع. 3: 387–390. DOI:10.1111/j.1745-6584.2003.tb02608.x. ISSN:1745-6584. مؤرشف من الأصل في 2015-12-03.
^ Barry، D. A؛ Parlange، J. -Y؛ Li، L (31 يناير 2000). "Approximation for the exponential integral (Theis well function)". Journal of Hydrology. ج. 227 ع. 1–4: 287–291. Bibcode:2000JHyd..227..287B. DOI:10.1016/S0022-1694(99)00184-5. مؤرشف من الأصل في 2013-03-16.

هذه بذرة مقالة عن التحليل الرياضي بحاجة للتوسيع. فضلًا شارك في تحريرها.

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