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Ramanujan Theta Functions -- from Wolfram MathWorld

Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It satisfies f(-1,a)=0 (2) and f(a,b) = f(b,a) (3) = (-a;ab)_infty(-b;ab)_infty(ab;ab)_infty (4) (Berndt 1985, pp. 34-35; Berndt et al. 2000), where (a;q)_k is a q-Pochhammer symbol, i.e., a q-series. A one-argument form of f(a,b) is also defined by f(-q) = f(-q,-q^2) (5) = (q;q)_infty (6) =...



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Ramanujan Theta Functions -- from Wolfram MathWorld

https://mathworld.wolfram.com/RamanujanThetaFunctions.html

Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It satisfies f(-1,a)=0 (2) and f(a,b) = f(b,a) (3) = (-a;ab)_infty(-b;ab)_infty(ab;ab)_infty (4) (Berndt 1985, pp. 34-35; Berndt et al. 2000), where (a;q)_k is a q-Pochhammer symbol, i.e., a q-series. A one-argument form of f(a,b) is also defined by f(-q) = f(-q,-q^2) (5) = (q;q)_infty (6) =...



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https://mathworld.wolfram.com/RamanujanThetaFunctions.html

Ramanujan Theta Functions -- from Wolfram MathWorld

Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It satisfies f(-1,a)=0 (2) and f(a,b) = f(b,a) (3) = (-a;ab)_infty(-b;ab)_infty(ab;ab)_infty (4) (Berndt 1985, pp. 34-35; Berndt et al. 2000), where (a;q)_k is a q-Pochhammer symbol, i.e., a q-series. A one-argument form of f(a,b) is also defined by f(-q) = f(-q,-q^2) (5) = (q;q)_infty (6) =...

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      Ramanujan Theta Functions -- from Wolfram MathWorld
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    • DC.Description
      Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It satisfies f(-1,a)=0 (2) and f(a,b) = f(b,a) (3) = (-a;ab)_infty(-b;ab)_infty(ab;ab)_infty (4) (Berndt 1985, pp. 34-35; Berndt et al. 2000), where (a;q)_k is a q-Pochhammer symbol, i.e., a q-series. A one-argument form of f(a,b) is also defined by f(-q) = f(-q,-q^2) (5) = (q;q)_infty (6) =...
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      Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It satisfies f(-1,a)=0 (2) and f(a,b) = f(b,a) (3) = (-a;ab)_infty(-b;ab)_infty(ab;ab)_infty (4) (Berndt 1985, pp. 34-35; Berndt et al. 2000), where (a;q)_k is a q-Pochhammer symbol, i.e., a q-series. A one-argument form of f(a,b) is also defined by f(-q) = f(-q,-q^2) (5) = (q;q)_infty (6) =...

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      Ramanujan Theta Functions -- from Wolfram MathWorld
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      Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It satisfies f(-1,a)=0 (2) and f(a,b) = f(b,a) (3) = (-a;ab)_infty(-b;ab)_infty(ab;ab)_infty (4) (Berndt 1985, pp. 34-35; Berndt et al. 2000), where (a;q)_k is a q-Pochhammer symbol, i.e., a q-series. A one-argument form of f(a,b) is also defined by f(-q) = f(-q,-q^2) (5) = (q;q)_infty (6) =...

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      Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It satisfies f(-1,a)=0 (2) and f(a,b) = f(b,a) (3) = (-a;ab)_infty(-b;ab)_infty(ab;ab)_infty (4) (Berndt 1985, pp. 34-35; Berndt et al. 2000), where (a;q)_k is a q-Pochhammer symbol, i.e., a q-series. A one-argument form of f(a,b) is also defined by f(-q) = f(-q,-q^2) (5) = (q;q)_infty (6) =...
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