Discovery Archive

Explore Ramanujan's Discoveries

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4 entries shown from 177 detailed discovery and contribution-family records.

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Partition Theory | 1919

p (5 n + 4) \equiv 0 (mod 5)

Ramanujan discovered striking congruence properties of partition numbers.

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Ramanujan's Master Theorem | 1918

\int_{0}^{\infty} x^{s - 1} ϕ (x) d x = \frac{π}{sin π s} ϕ (- s)

Ramanujan's Master Theorem is catalogued as a theorem in Ramanujan's Master Theorem.

Plain language: A central formula or notation associated with Ramanujan's Master Theorem.

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Prime-Number Theory

Contribution family

Ramanujan's Prime-Interval Theorem is catalogued as a theorem in Prime-Number Theory.

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q-Series and Basic Hypergeometric Series

_{1} ψ_{1} (a; b; q, z) = n = - \infty \sum \infty \frac{( a ; q ) _{n}}{( b ; q ) _{n}} z^{n}

Ramanujan's 1 psi 1 Summation is catalogued as a theorem in q-Series and Basic Hypergeometric Series.

Plain language: A central formula or notation associated with Ramanujan's 1 psi 1 Summation.

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