Difference between revisions of "Derivative of Jacobi theta 1 at 0"
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(Created page with "==Theorem== The following formula holds: $$\vartheta_1'(0,q)=\vartheta_2(0,q) \vartheta_3(0,q) \vartheta_4(0,q),$$ where $\vartheta_1$ denotes the Jacobi theta 1, $\varthe...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3|next= | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3|next=Logarithmic derivative of Jacobi theta 1 equals cotangent + a sum of sines}}: 16.28.6 |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 07:10, 27 June 2016
Theorem
The following formula holds: $$\vartheta_1'(0,q)=\vartheta_2(0,q) \vartheta_3(0,q) \vartheta_4(0,q),$$ where $\vartheta_1$ denotes the Jacobi theta 1, $\vartheta_2$ denotes the Jacobi theta 2, $\vartheta_3$ denotes Jacobi theta 3, and $\vartheta_4$ denotes Jacobi theta 4.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 16.28.6
