Logarithmic integrals with applications to BBP and Euler-type sums
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Publication:2699585
DOI10.1007/s40840-023-01485-3OpenAlexW4361217462MaRDI QIDQ2699585
Publication date: 19 April 2023
Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2302.06640
gamma functionharmonic numberspolygamma functionsdefinite integralslogarithmic integralsBBP-type series
Gamma, beta and polygamma functions (33B15) Special sequences and polynomials (11B83) Hurwitz and Lerch zeta functions (11M35) Antidifferentiation (26A36)
Cites Work
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- New formulae of BBP-type with different moduli
- Evaluation of integrals with hypergeometric and logarithmic functions
- Harmonic-binomial Euler-like sums via expansions of \((\arcsin x)^p\)
- On the computation and verification of \(\pi\) using BBP-type formulas
- On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions
- The polygamma function \(\psi^{(k)}(x)\) for \(x={1\over 4}\) and \(x={3\over 4}\)
- Discovering and Proving Infinite Binomial Sums Identities
- On the rapid computation of various polylogarithmic constants
- A restricted Epstein zeta function and the evaluation of some definite integrals
- Convolution identities involving the central binomial coefficients and Catalan numbers
- On the genesis of BBP formulas
- Some BBP-type series for polylog integrals
- A natural companion to Catalan's constant
- Alternating Euler sums and BBP-type series
- Parameterized families of polylog integrals
- Values of the polygamma functions at rational arguments
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