Not to be confused with the mock theta functions discovered by Ramanujan.
In mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. In particular, the Jacobi triple product takes on a particularly elegant form when written in terms of the Ramanujan theta. The function is named after mathematician Srinivasa Ramanujan.
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mathematics, particularly q-analog theory, the Ramanujanthetafunction generalizes the form of the Jacobi thetafunctions, while capturing their general properties...
In mathematics, thetafunctions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces...
unconventional results, such as the Ramanujan prime, the Ramanujanthetafunction, partition formulae and mock thetafunctions, have opened entire new areas...
mock thetafunction is essentially a mock modular form of weight 1/2. The first examples of mock thetafunctions were described by Srinivasa Ramanujan in...
the sum of triangular numbers are connected to thetafunctions, in particular the Ramanujanthetafunction. The sum of two consecutive triangular numbers...
Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series. Although the Ramanujan...
trigonometric functions. For example, if x = sin θ {\displaystyle x=\sin \theta } , then d x / d θ = cos θ = 1 − x 2 , {\textstyle dx/d\theta =\cos \theta ={\sqrt...
connections and consistent notation with the Ramanujan G- and g-functions and the Jacobi thetafunctions, both of which conventionally uses the nome....
result concerning infinite products is that every entire function f(z) (that is, every function that is holomorphic over the entire complex plane) can be...
Srinivasa Ramanujan, Greatest Indian mathematician who compiled Ramanujan prime, the Ramanujanthetafunction, partition formulae and mock thetafunctions and...
" Ramanujan, Question 723, Papers p. 332 Somu, Sai Teja; Kukla, Andrzej (2022). "On some generalizations to floor function identities of Ramanujan" (PDF)...
Arithmetic functions are often extremely irregular (see table), but some of them have series expansions in terms of Ramanujan's sum. An arithmetic function a is...
zeta function Generalized Riemann hypothesis Lehmer pair Prime zeta function Riemann Xi function Renormalization Riemann–Siegel thetafunction ZetaGrid...
enjoys a particularly elegant form when expressed in terms of the Ramanujanthetafunction. For | a b | < 1 {\displaystyle |ab|<1} it can be written as ∑...
\eta } is the Dedekind eta function. For the Fourier coefficients of Δ {\displaystyle \Delta } , see Ramanujan tau function. e 1 {\displaystyle e_{1}}...
{R} )} . An example is the Jacobi thetafunction θ ( z , τ ) = ∑ n = − ∞ ∞ e 2 π i n z + i π n 2 τ {\displaystyle \theta (z,\tau )=\sum _{n=-\infty }^{\infty...
Kosaraju suggested it in 1978. Ramanujanthetafunction, Ramanujan prime, Ramanujan summation, Ramanujan graph and Ramanujan's sum – Discovered by the Indian...
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