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:<math>\left[\frac{2\lambda^*(x)}{1-\lambda^*(x)^2}\right]^{1/2} - \left[\frac{2\lambda^*(25x)}{1-\lambda^*(25x)^2}\right]^{1/2} = 2\left[\frac{2\lambda^*(x)}{1-\lambda^*(x)^2}\right]^{1/12}\left[\frac{2\lambda^*(25x)}{1-\lambda^*(25x)^2}\right]^{1/12} + 2\left[\frac{2\lambda^*(x)}{1-\lambda^*(x)^2}\right]^{5/12}\left[\frac{2\lambda^*(25x)}{1-\lambda^*(25x)^2}\right]^{5/12} </math>
:<math>a^{8}+b^{8}-7a^4b^4 = 2\sqrt{2}ab+2\sqrt{2}a^7b^7\, \left(a = \left[\frac{2\lambda^*(x)}{1-\lambda^*(49xx)^2}\right]^{1/412}\right) +\left(b = \left[1-\frac{2\lambda^*(x49x)^2]^}{1/8}[1-\lambda^*(49x)^2}\right]^{1/812} = 1\right) </math>
:<math>a^{12}-bc^{12} = 4\sqrt{2}abac+22\sqrt{2}a^3b3c^3+44\sqrt{2}a^5b5c^5+44\sqrt{2}a^7b7c^7+22\sqrt{2}a^9b9c^9+4\sqrt{2}a^{11}bc^{11}\, \left(a = \left[\frac{2\lambda^*(x)}{1-\lambda^*(x)^2}\right]^{1/12}\right) \left(bc = \left[\frac{2\lambda^*(121x)}{1-\lambda^*(121x)^2}\right]^{1/12}\right) </math>
:<math>(a^2-cd^2)(a^4+cd^4-7a^2c2d^2)[(a^2-cd^2)^4-a^2c2d^2(a^2+cd^2)^2] = 8ac8ad+8a^{13}cd^{13}\, \left(a = \left[\frac{2\lambda^*(x)}{1-\lambda^*(x)^2}\right]^{1/12}\right) \left(cd = \left[\frac{2\lambda^*(169x)}{1-\lambda^*(169x)^2}\right]^{1/12}\right) </math>
These are the relations between lambda-star and the Ramanujan-G-function:
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