Integral evaluation through the binomial formula and differentiation techniques

الموضوعات

علوم بحتة وطبيعية

الملخص

In the realm of mathematics, the evaluation of integrals plays a crucial role in various fields such as physics, engineering, and economics. Integrals represent the accumulation of quantities over a continuous range and are essential for understanding the behavior of functions and solving complex problems. Over the years, mathematicians and researchers have developed numerous techniques to evaluate integrals efficiently and accurately. This thesis consists of two parts. In the first part, we present some binomial identities, special numbers and polynomials as well as basic formulas related to Euler’s transformation of series, Handamard’s series multiplication theorem and several transformation formulas with example and applications. These theoretical tools will be used to gain a better understanding of the second part of this thesis which explores two different techniques for evaluating integrals. The first technique uses a special formula to transform integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integral. The second technique is by differentiation with respect to a parameter.

روابط وملفات

التعريف والنوع

رقم الوثيقة

0c83589d-2ccd-44aa-9e1a-3be9ac0d36be

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل ماجيستير

نوع الملف

pdf text

أسماء الملفات

794159_1.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":"Ghewa Zgheib","title_ar":"اعداد","title_en":"Preparation"},{"name_ar":"Roger Nakad ","title_ar":"اشراف","title_en":"Supervision"}]

اللغة

English

المصدر والدورية

اسم المصدر

Integral evaluation through the binomial formula and differentiation techniques

المحتوى والصفحات

عدد الصفحات

0

كلمات الباحثين

Equations, Binomial

إشراف وإعداد

الإشراف

Roger Nakad

الإعداد

Ghewa Zgheib

الاقتباسات الببليوغرافية