I want the details about the number of bernoulli and all of related to the expansion of Euler-Maclaurin
Thank You
For a summary of Bernoulli polynomials and numbers, you can consult any good textbook in numerical analysis or any good handbook, e.g.," NBS Handbook of Mathematical Functions, "NIST Handbook of Mathematical Functions," both of which can be accessed online. You can also consult Appendix D in my book "Practical Extrapolation Methods : Theory and Applications," where you can also find almost everything known until 2000, including Euler-Maclaurin expansions for integrals with algebraic and/or logarithmic singularities.
Since then I published three papers that generalize Euler-Maclaurin expansions to functions with arbitrary algebraic and/or logarithmic singularities, and three more papers dealing with their application to Cauchy principal value integrals and Hadamard Finite Part integrals. You can access them all on researchgate. For your convenience, I am attaching them here.
All the best.
You might start with this.
https://www.researchgate.net/publication/226112113_Euler-Maclaurin_expansions_for_integrals_with_endpoint_singularities_A_new_perspective
Article Euler-Maclaurin expansions for integrals with endpoint singu...
For a summary of Bernoulli polynomials and numbers, you can consult any good textbook in numerical analysis or any good handbook, e.g.," NBS Handbook of Mathematical Functions, "NIST Handbook of Mathematical Functions," both of which can be accessed online. You can also consult Appendix D in my book "Practical Extrapolation Methods : Theory and Applications," where you can also find almost everything known until 2000, including Euler-Maclaurin expansions for integrals with algebraic and/or logarithmic singularities.
Since then I published three papers that generalize Euler-Maclaurin expansions to functions with arbitrary algebraic and/or logarithmic singularities, and three more papers dealing with their application to Cauchy principal value integrals and Hadamard Finite Part integrals. You can access them all on researchgate. For your convenience, I am attaching them here.
All the best.
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