Integrals and Seriesby Shobhit Bhatnagar

The notebook

All articles

29 explorations in mathematics.

  1. Lobachevsky-type logarithmic integrals via partial-fraction series
  2. A difference of arctangent integrals and dilogarithm identities
  3. The inverse tangent integral at two minus root three
  4. An integral involving the squared arctangent of sine squared
  5. Evaluating a logarithmic Fresnel integral by differentiating under the integral sign
  6. A logarithmic sine integral via a keyhole contour
  7. A trigonometric integral via a semicircular contour
  8. Mellin transforms of sine and cosine via a quarter-circle contour
  9. The Fourier transform of the hyperbolic secant
  10. A real integral evaluated over a rectangular contour
  11. An algebraic integral with a fifth root via the beta function
  12. A parametric beta integral with a shifted linear denominator
  13. A proof of GR 3.255
  14. Integral representations of the reciprocal beta function
  15. Introduction to Theta Functions II
  16. Introduction to Theta Functions I
  17. When is the group of units in the integers modulo n cyclic?
  18. Evaluating very nasty logarithmic integrals: Part III
  19. Evaluating very nasty logarithmic integrals: Part II
  20. Evaluating very nasty logarithmic integrals: Part I
  21. Euler sums involving squared harmonic numbers
  22. A contour integration approach to infinite series
  23. An alternating Euler Sum
  24. Ramanujan's Master Theorem: Part I
  25. Fourier Series of the Log-Gamma Function and Vardi's Integral
  26. Bernoulli numbers and a related integral
  27. Weyl's Equidistribution Theorem
  28. Eisenstein's Proof of Quadratic Reciprocity
  29. Simplification of Incomplete Beta Functions