Indian Contributions to Calculus in the 19th and 20th Centuries

Srinivasa Ramanujan is widely regarded as the father of modern Indian mathematics for his groundbreaking work in number theory, analysis, and other areas of mathematics.

Harish-Chandra made fundamental contributions to the theory of modular forms, representation theory, and harmonic analysis.

C. R. Rao is known for his work in statistics, including the Rao-Blackwellization theorem, which provides a method for improving the efficiency of estimators.

S. N. Bose is renowned for his work on quantum statistics, particularly the Bose-Einstein statistics, which describes the behavior of bosons.

Srinivasa Ramanujan made significant contributions to the study of the Riemann zeta function and the theory of partitions, leaving behind a wealth of mathematical insights.

Harish-Chandra's work on automorphic forms had a profound impact on the field, leading to new insights and advancements.

C. R. Rao is credited with developing the theory of information geometry, which provides a geometric framework for studying statistical problems.

Harish-Chandra made significant contributions to the theory of Lie groups, including the development of the Harish-Chandra modules.

Harish-Chandra's work on the theory of distributions, also known as generalized functions, had a major impact on analysis and its applications.

C. R. Rao made significant contributions to the theory of probability, including the development of the Cramér-Rao inequality and the Rao-Blackwellization theorem.

Srinivasa Ramanujan's work on the theory of numbers, including his discovery of the Ramanujan prime and the Ramanujan theta function, revolutionized the field.

Srinivasa Ramanujan made significant contributions to the theory of functions, including the development of the Ramanujan master theorem and the Ramanujan summation formula.

Srinivasa Ramanujan made important contributions to the theory of differential equations, including the development of the Ramanujan differential equation and the Ramanujan-Sato differential equation.

Srinivasa Ramanujan made important contributions to the theory of integral equations, including the development of the Ramanujan integral equation and the Ramanujan-Mellin integral equation.

C. R. Rao made significant contributions to the theory of matrices, including the development of the Rao-Blackwellization theorem and the Rao-Cramer inequality.