Ramanujan's Theta Functions

1. Sum to Product Identities
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2. Elliptic Functions
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3. Transformations
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4. Theta Functions
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5. Levels 1, 2, 3, and 4: Jacobi’s Inversion Theorem and Ramanujan’s Alternative Theories
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6. Level 5: The Rogers–Ramanujan Continued Fraction
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7. Level 6: Ramanujan’s Cubic Continued Fraction
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8. Level 7
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9. Level 8: The Ramanujan–Göllnitz–Gordon Continued Fraction
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10. Level 9
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11. Level 10: Ramanujan’s Function k

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12. Levels 11 and 23
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13. Level 12
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14. Hypergeometric Modular Transformations
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15. Ramanujan’s Series for 1∕π

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Avainsanat: Mathematics, Number Theory, Algebraic Geometry