New mathematical insights and rigorous results are often gained through extensive
experimentation using numerical examples or graphical images and analyzing them. Today …

When I am asked what sort of mathematics I do, I say “High School algebra, but taken
somewhat further”. This is the study and application of q-series, technically known as basic …

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop quantum
chromodynamics corrections to the ρ-parameter. They obey non-factorizing differential …

1 X nD 1 qn2 xn; where jqj< 1 and 0< jxj< 1; or a generalization or specialization of such a
series. Theta functions were studied extensively by Ramanujan and form the central theme …

In geometric function theory, generalized elliptic integrals and functions arise from the
Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are …

In his famous paper on modular equations and approximations to $\pi $, Ramanujan offers
several series representations for $1/\pi $, which he claims are derived from" corresponding …

This book provides algorithms and ideas for computationalists. Subjects treated include low-
level algorithms, bit wizardry, combinatorial generation, fast transforms like the Fourier …

There is a beautiful cubic analogue of Jacobi's fundamental theta function identity: $\theta
_3^ 4=\theta _4^ 4+\theta _2^ 4$. It is\[{\left ({\sum\limits _ {n, m=-\infty}^\infty {{q^{{n^ 2}+ …

When we pause to reflect on Ramanujan's life, we see that there were certain events that
seemingly were necessary in order that Ramanujan and his mathematics be brought to …

There are three modular forms a (q), b (q), c (q) involved in the parametrization of the
hypergeometric function analogous to the classical θ2 (q), θ3 (q), θ4 (q) and the …