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 List of Basic Maths Formulas for Class 5 to 12 Integrals Maths Formulas for Class 12 Chapter 7 Applications of Integrals Maths Formulas for Class 12 Chapter 8 Maths Formulas for Class 12 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 Post21 hours ago Building the Right Strategy for a Successful Business Guest Post2 days ago 6 Ways to Keep Your Business Moving After Bankruptcy Guest Post2 days ago Top Things All Students Should Know About Their Life Guest Post3 days ago How To Make A Perfect College Essay Guest Post2 weeks ago Words With Friends Dictionary: Learn More Than You Ever Wanted To Know About Words Paryayvachi2 weeks ago Dharti Ka Paryayvachi Shabd Guest Post3 weeks ago How To Write a Good History Essay Guest Post1 month ago 6 Reasons Why You Should Trade With Evotrade English Vocabulary1 month ago English Grammar Rules & Usage Guest Post2 months ago Some of the Core Functions of HR that You Should Know Math2 years ago List of Basic Maths Formulas for Class 5 to 12 Math3 years ago What is (a-b)^3 Formula? a^3-b^3 Formula | (a-b)^2 | (a+b-c)^2 English Vocabulary2 years ago Animals Name for Kids in English and Hindi with Pictures Math4 years ago Percentage Formulas | How to Calculate Percentages of a Number? Math4 years ago Y Intercept & X Intercept Formula | Slope Intercept Form & Equation English Vocabulary2 years ago Vegetables Name In English And Hindi With Pictures Math3 years ago What Is Loan Amortization Formula? Calculation & Example? Math2 years ago Average Rate Of Change Formula Made Simple Math4 years ago What is Integration? List of Integration by Parts Formulas Questions2 years ago What is The Formula of Cos(a+b)? Advertisement Important Maths Formula Direction Of A Vector Formula Probability Distribution Formula Quartile Formula Circumference of a Circle Formula Decay Formula Margin of Error Formula Population Mean Formula Infinite Geometric Series Formula Double Time Formula Linear Approximation Formula Cosine Formula Spherical Segment Formula Proportion Formula Rectangular Prism Formula R Squared Formula Triangular Prism Formula Statistical Significance Formula Difference of Squares Formula Vertex Formula Perfect Square Formula Vieta Formula Right Angle Formula U Substitution Formula Percentage Change Formula Regular Square Pyramid Formula Gross Profit Formulas Trajectory Formula Exponential Formulas Sample Mean Formula Quotient Formulas Real Number Box Formulas Simple Interest Formula X& Y Intercept Formulas Triangular Pyramid Formula Coefficient Formulas Distance Formula Arithmetic Sequence Formulas Weighted Mean Formula Parallelogram Formulas Multiplication Table Pentagon Formulas Volume Of Parallelepiped Formula Octagon Formulas Volume Of An Ellipsoid Formula Binary Formulas Volume Of A Square Pyramid Formula Binomial Formulas Charge Density Formula Isosceles Triangle Formulas Complex Number Power Formula Equilateral Triangle Formulas Diagonal Formula Triangle Formulas Division Formula Area of Cube Formulas Diameter Formula Sphere Formulas Coin Toss Probability Formula Trapezoid Formulas Circle Graph Formula Hexagon Formulas Chord Length Formula Cube Formulas Cofunction Formulas Discount Formulas Cofactor Formula Rhombus Formulas Cpk Cp Formula Cone Formulas Degree And Radian Measure Formula Equation Formulas Consecutive Integers Formula Cylinder Formulas Interpolation Formula Pythagoras Formulas Prime Number formula Matrix Formulas Euler Maclaurin formula Area of Circle Formulas Frequency Distribution formula Circle Formulas Hypergeometric Distribution formula Compound Interest Formulas Implicit Differentiation formula Completing the Square Formulas Inverse Function formula Square Formulas Inverse Hyperbolic Functions formula Factorial Formulas Pearson Correlation formula Statistics Formulas Confidence Interval formula Linear Formulas Lagrange Interpolation formula Derivative Formulas Hypothesis Testing formula Differentiation Formulas Kite formula Pyramid Formulas Degrees of Freedom formula Rectangle Formulas Interquartile Range formula Probability Formulas Function Notation formula Mean Median Mode Formulas Gaussian Distribution formula Vector Formulas Hyperbolic Function formula Ellipse Formulas What Is Numbers? Permutation & Combination Formulas Area under the Curve Formula Complex Number Formulas Axis of Symmetry Formula Calculus Formulas Arithmetic Progression Formula Integration Formulas Average Deviation Formula Trigonometry Formulas Equation of a Circle Formula Polynomial Formulas Chain Rule Formula Geometry Formulas Quadratic Interpolation Formula Algebra Formulas Change of Base Formula LCM Formulas Absolute Value Formula Percentage Formulas Discriminant Formula Effect Size Formula