Author

Luc Ramsès Talla Waffo

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Preprint Aug 2026

Dirichlet Beta Analogues, Sign Alternation, and Lerch Unification of Hyperbolic and Logarithmic Tangent Integrals

We develop a Dirichlet-beta counterpart and a structural extension of the coefficient-extraction framework for hyperbolic and logarithmic tangent integrals. For integers $m\geq n\geq1$ with $m+n$ even, the zeta-type formula \[ \int_0^\infty\frac{\tanh^{m+1}x}{x^{n+1}}\,dx = (-1)^{(m-n)/2} \sum_{p=\lceil n/2\rceil}^{(m+...

Luc Ramsès Talla Waffo · 1 citation

Preprint Sep 2026

From Umbral Hyperbolic Integrals to a Cotangent Coefficient Formula for the Mittag Leffler Polynomials

Let $g_n(x)$ be the Mittag--Leffler polynomials defined by $$ \sum_{n\ge0}g_n(x)t^n=\frac12\left(\frac{1+t}{1-t}\right)^x. $$ We derive the coefficient formula $$ g_n(x)=\frac1n\sum_{j=0}^{\lfloor (n-1)/2\rfloor} (-1)^j\frac{2^{n-2j-1}}{(n-2j-1)!} [u^{2j}](u\cot u)^n\,x^{n-2j}, $$ equivalently $$ [u^{n-r}](u\cot u)^n...

Luc Ramsès Talla Waffo · 0 citations