Independent materials developed from my work on integrals and special functions. These currently include the themed ODE-Integration Bee slide series “Elementary Special Functions & Integrals via ODE Conversions” and accompanying Mathematica notebooks or packages that use results from my research to produce closed forms and identities that standard computer algebra systems do not generate on their own. As new materials are completed, they will be added here.
A themed sequence of talks developed for the ODE-Integration Bee. Each session focuses on a classical special function and shows how families of integrals can be solved by turning them into differential equations.
This session introduces the Gamma function and the Gaussian integral, and shows how an integral can be treated as a function of a parameter, differentiated, and turned into an ODE. The slides include worked examples and Bee-style problems.
This session develops the Beta function, builds its connection with the Gamma function, and shows how classical Euler-type integrals can be evaluated through simple substitutions. The ODE conversion idea appears again in this new setting, with examples crafted in the spirit of the Bee.
Mathematica material developed from my work on integrals and special functions. These notebooks and packages use results from my research to obtain closed forms and identities that standard computer algebra systems do not generate on their own.
Initial public release of MalmstenIntegralSequences, a Wolfram Language package accompanying joint research work of Abdulhafeez A. Abdulsalam and Michael J. Schlosser on Malmsten-type integral sequences and related nested-sum identities. It includes reusable symbolic computation tools for closed forms, coefficient vectors, Hurwitz-zeta derivative reductions, symbolic and numerical evaluation routines, verification utilities, and test scripts.
A self-contained Mathematica notebook built on results from my research on Malmsten’s integral and related integrals. It generates closed forms for integrals that computer algebra systems do not produce on their own.