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Papers - notes on Combinatorial sums - identities and Binomial coefficients in general

  1. Alternating Sums of the Reciprocals of the Binomial Coefficients - H.Belbachir M.Rahmani B.Sury (Journal of Integer Sequences)
  2. Combinatorial Identities and Inverse Binomial Coefficients - T.Mansour
  3. Combinatorial Sums and Implicit Riordan Arrays - D.Merlini R.Sprugnoli M.C.Verri
  4. Combinatorial Sums and Series Involving Inverses of Binomial Coeffecients - T.Trif (Fibonacci Quarterly)
  5. Combinatorial Sums Egorychevs Method of Coefficients and Riordan Arrays - Christoph Furst (Master Thesis)
  6. Abel Binomial Theorem
  7. Identities Involving Reciprocals of Binomial Coeffecients - B. Sury (Journal of Integer Sequences)
  8. Interesting Series involving the Central Binomial Coefficient - D.H.Lehmer (AMM)
  9. Riordan arrays and combinatorial sums - R.Sprugnoli (Discrete Mathematics)
  10. Series with Central Binomial Coefficients Catalan Numbers and Harmonic Numbers - K.N.Boyadzhiev (Journal of Integer Sequences)
  11. Sums of Reciprocals of The Central Binomial Coeffficients - R.Sprugnoli (Electronic Journal of Combinatorial Number Theory)
  12. The Method of Coefficients - D.Merlini R.Sprugnoli M.Cecilia Verri
  13. Riordan Array Proofs of Identities in Goulds Book - R.Sprugnoli
  14. An Introduction to Mathematical Methods in Combinatorics - R.Sprugnoli
  15. Generatingfunctionology - H.S.Wilf
  16. Concrete Mathematics - Graham Knuth Patashnik
  17. On certain series involving reciprocals of binomial coefficients - N.Batir (Journal of Classical Analysis)
  18. Formal Power Series - I.Niven (The American Mathematical Monthly)
  19. Summation Formulas Involving Binomial Coefficients, Harmonic Numbers and Generalized Harmonic Numbers - J.Choi (Hindawi P.C. Abstract and Applied Analysis)
  20. Combinatorial Sums And Finite Differences - M.Z.Spivey
  21. Binomial Transform And The Backward Difference - K.Boyadzhiev (arxiv.org)
  22. Power Sum Identities With Generalized Stirling Numbers - K.N.Boyadzhiev (arxiv.org)

Sums of Trigonometric powers

  1. A Note On Cosine Power Sums - M.Merca (Journal Of Integer Sequences)
  2. Finite Trigonometric Product and Sum Identities - M.Chamberland (Fibonacci Quarterly August 2012)
  3. Fourier Transforms and Trigonometric Sums
  4. On Some Trigonometric Power Sums - H.Chen (IJMMS)
  5. Some Remarks on Problem U23 - D.Andrica M.Piticari (Mathematical Reflections 2008 - 4)
  6. Some relevant references on AOPS:

The Integrals in Gradshteyn and Ryzhik (SCIENTIA)

  1. A family of logarithmic integrals
  2. Elementary logarithmic integrals
  3. Combinations of logarithms and exponentials
  4. The gamma function
  5. Some trigonometric integrals
  6. The beta function
  7. Elementary examples
  8. Combinations of powers exponentials and logarithms
  9. Combinations of logarithms rational and trigonometric functions
  10. The digamma function
  11. The incomplete beta function
  12. Some logarithmic integrals
  13. Trigonometric forms of the beta function
  14. An elementary evaluation of entry 3.411.5
  15. Frullani integrals
  16. Complete elliptic integrals
  17. The Riemann zeta function
  18. Some automatic proofs
  19. The error function
  20. Hypergeometric functions
  21. Hyperbolic functions
  22. Bessel-K functions
  23. Combination of logarithms and rational functions
  24. Polylogarithm functions
  25. Evaluation by series

Series summation and related topics

  1. The Sum of the Harmonic Series Is Not Enough - O.Kouba (SIAM)
  2. The Sum Of Certain Series Related To Harmonic Numbers O.Kouba (Arxiv.org - Octogon Magazine)
  3. A Generalization of Riemann Sums - O.Kouba (Mathematical Reflections 2010-1)
  4. Evaluation of Some Variant Euler Sums - H.Chen (Journal of Integer Sequences)
  5. On a Series of Furdui and Quin and Some Related Integrals - K.N.Boyadzhiev (Arxiv.org)
  6. On The Summation of Certain Iterated Series - O.Furdui T.Trif (Journal of Integer Sequences)
  7. Some Series Of The Zeta And Related Functions - V.S.Adamchik H.M.Srivastava
  8. Some Identities Involving Harmonic Numbers - J.Spieß Mathematics Of Computation

Integrals and related topics

  1. A Mixed Parseval-Plancherel Formula - O.Kouba
  2. Exact Evaluation Of Some Highly Oscillatory Integrals - O.Kouba

Special Functions - Constants

  1. Representations Of Catalan's Constant - D.M.Bradley
  2. Introduction to the Gamma Function - P.Sebah X.Gourdon
  3. Inequalities for the Polygamma Functions with Application - Chao-Ping Chen

Asymptotics

  1. Preliminaries
  2. An introduction to asymptotic analysis - S.J.A.Malham
    • Problems and solutions relevant to the notes above can be found here.
  3. Asymptotic Methods in Analysis
  4. Asymptotics of Implicit Functions and Computer Algebra - B.Salvy
  5. Asymptotics of Recurrent Sequences - M.Omarjee
  6. Asymptotic Analysis and Perturbation Theory - K.G.Lamb
  7. Method Of Dominant Balance
  8. ODE and Singular Points
  9. Asymptotic Enumeration Methods - A.M.Odlyzko
  10. Lecture Notes on Asymptotic Expansions - I.Avramidi
  11. Mathematics For The Physical Sciences - H.S.Wilf
  12. Asymptotic Methods in Enymeration - E.A.Bender (SIAM Review)
  13. Singularity Analysis Of Generating Functions - P.Flajolet A.Odlyzko (SIAM Journal Of Discrete Mathematics)
  14. Asymptotic Expansions for Integrals - G.Nemes (M.Sc.)
  15. Effective Asymptotics For Some Nonlinear Recurrences And Almost Doubly-Exponential Sequences - E.Ionascu P.Stanica (Acta Math. Univ. Comenianae)
  16. Mellin Transforms and Asymptotics. Finite Differences and Rice's Integrals - P.Flajolet R.Sedgewick (Theoretical Computer Science)
  17. An Asymptotic Formula for Binomial Sums - R.J.MacIntosh (Journal Of Number Theory)

  1. Computation of various integrals where the Euler's constant appears (By M.Omarjee).
  2. A collection of problems and basic propositions, regarding limits, mostly been discussed on the www.artofproblemsolving.com forum. (By the member pain rinnegan).
  3. Various Mean Value Theorems. By Cezar Lupu and Tudorel Lupu.

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