TOPICS
Search

Ramanujan chi-Function

The Ramanujan chi-function is the function defined for |q|<1 by

chi(q)=(-q;q^2)_infty
(1)
=product_(k=0)^(infty)(1+q^(2k+1))
(2)
=1+q+q^3+q^4+q^5+q^6+q^7+2q^8+...
(3)

(OEIS A000700; Berndt 1991, p. 37), where (a;q)_infty is a q-Pochhammer symbol.

The Ramanujan g- and G-functions satisfy

G_n=2^(-1/4)q^(-1/24)chi(q)
(4)
g_n=2^(-1/4)q^(-1/24)chi(-q)
(5)

(Andrews and Berndt 2005, p. 66), where q=e^(-pisqrt(n)) and n>0.

See also

q-Pochhammer Symbol, Ramanujan g- and G-Functions, Ramanujan Theta Functions

Explore with Wolfram|Alpha

References

Andrews, G. E. and Berndt, B. C. Ramanujan's Lost Notebook, Part I. New York: Springer, p. 66, 2005.Berndt, B. C. Ramanujan's Notebooks, Part III. New York: Springer-Verlag, p. 37, 1991.Sloane, N. J. A. Sequence A000700 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Ramanujan chi-Function

Cite this as:

Weisstein, Eric W. "Ramanujan chi-Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RamanujanChi-Function.html

Subject classifications