Math Euler Maclaurin Formula with Problem Solution & Solved Example More Videos The Euler–Maclaurin formula in mathematics provides a powerful relationship between sums and integrals. This is also good to measure the integrals approximation by finite sums or you could evaluate the sum of a finite series or infinite series conversely with the helps of integral or calculus. For example, this is possible to derive a plenty of asymptotic expansions with the help of the Euler–Maclaurin formula and the sum of powers is an immediate consequence here. \[\large \sum_{k=p}^{m-1}\phi (k)=\int_{p}^{m}\phi (t)dt+\sum_{v=1}^{n-1}\frac{B_{v}}{v!}(\phi^{v-1}m-\phi^{v-1}p)+R_{n}\] Where, B_{v}=Bernoulli numbers R_{n}=remainder The formula was first discovered in 1735 independently by Leonhard Euler and Colin Maclaurin. Euler was working on slowly converging infinite series that can be further used to calculate integrals. Then he derived one formula to provide relationship among sum or differences of integrals in terms of higher derivatives. The formula was derived using repeated integrations by parts to the successive intervals for integers. This popular derivation is largely based on periodic Bernoulli functions, that are generally defined in terms of Bernoulli polynomials. This formula is suitable to find detailed error analysis too in numerical quadrature. This is based on the superior performance of trapezoid rule as per smooth periodic function and they are needed on certain extrapolation methods too. The results calculated from the Euler–Maclaurin formula are highly accurate based on discrete cosine transformation. The technique is also named as the periodic transformations. Hence, this is clear that Euler–Maclaurin formula is powerful method for approximation related to the series summation to the continuous integral of a function. To understand the Euler–Maclaurin formula deeply, you should understand the Bernoulli polynomials first and move ahead. Related posts: What is Integration? List of Integration by Parts Formulas Integrals Maths Formulas for Class 12 Chapter 7 Infinite Geometric Series Formula, Hyper Geometric Sequence Distribution List of Basic Maths Formulas for Class 5 to 12 Applications of Integrals Maths Formulas for Class 12 Chapter 8 Maths Formulas for Class 12 Sequences and Series Formulas for Class 11 Maths Chapter 9 Maths Formulas For Class 11 Definite Integral Formula Polynomials Formulas for Class 9 Maths Chapter 2 List of Maths Formulas for Class 10th CBSE Statistics Formulas for Class 10 Maths Chapter 14 Polynomials Formulas for Class 10 Maths Chapter 2 What is Polynomial? List of Basic Polynomial Formula U Substitution Formula – Problem Solution with Solved Example Prime Number Formula with Problem Solution & Solved Example Relations and Functions Formulas for Class 11 Maths Chapter 2 Three Dimensional Geometry Maths Formulas for Class 12 Chapter 11 Right Angle Formula| Half-Angle, Double Angle, Multiple Difference of Squares Formula | Regression Sum of Squares Formula Related Topics: Up Next Prime Number Formula with Problem Solution & Solved Example Don't Miss Frequency Distribution Formula with Problem Solution & Solved Example Continue Reading Latest Popular Guest Post12 hours ago How Machine Learning Changed The Traditional Ways Of Developing A Mobile App. Guest Post1 day ago Why Email Marketing Is Important For Ecommerce Business? Difference Between5 days ago How to Compare Vagrant, Kubernetes, Mesos, and Docker? Learn5 days ago Square and Square Root Table of 1 to 100 | 100 Square Root Chart Learn5 days ago How Many Seconds in a Minutes, Hour, Day, Week, Month and Year? Learn5 days ago How Many Hours in a Day, Week, Month and Year or Leap Year? Difference Between5 days ago Difference Between Apache Spark and Apache Flink Guest Post3 weeks ago Top 12 Big Data Certifications in Demand For 2020 Difference Between3 weeks ago Node.js vs React.js: Which One Should You Opt For? Math1 month ago NCERT CBSE Class 6 Maths Chapter 2 Whole Numbers Introduction Math8 months ago Average Rate Of Change Formula Made Simple Math8 months ago List of Basic Maths Formulas for Class 5 to 12 Math2 years ago Percentage Formulas | How to Calculate Percentages of a Number? Math2 years ago Surface Area of a Triangular Prism Formula & Volume of a Triangular Math2 years ago Triangular Pyramid Formula | Volume & Surface Area of a Triangular Pyramid Math2 years ago Y Intercept & X Intercept Formula | Slope Intercept Form & Equation Math2 years ago What is Integration? List of Integration by Parts Formulas Math8 months ago List of Basic Algebra Formulas for Class 5 to 12 Math2 years ago List of Pyramid Formula – Surface Area, Volume of Pyramid Math2 years ago What is (a-b)^3 Formula? a^3-b^3 Formula | (a-b)^2 | (a+b-c)^2 Advertisement