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- 00:06, 26 June 2016 (diff | hist) . . (+307) . . N Closed form for partition function with sinh (Created page with "==Theorem== ==Proof== ==References== * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Generating function for parti...")
- 00:00, 26 June 2016 (diff | hist) . . (-5) . . Generating function for partition function
- 23:59, 25 June 2016 (diff | hist) . . (+536) . . N Generating function for partition function (Created page with "==Theorem== The following formula holds for $|x|<1$: $$\displaystyle\sum_{k=0}^{\infty} p(k) x^k = \displaystyle\prod_{k=1}^{\infty} \dfrac{1}{1-x^n}=\dfrac{1}{\displaystyle\s...")
- 23:56, 25 June 2016 (diff | hist) . . (+50) . . Partition
- 22:33, 25 June 2016 (diff | hist) . . (+148) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 22:18, 25 June 2016 (diff | hist) . . (+6) . . Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1 (current)
- 22:17, 25 June 2016 (diff | hist) . . (+475) . . N Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1 (Created page with "__NOTOC__ ==Theorem== The following formula holds for $\mathrm{Re}(z)>k+1$: $$\displaystyle\sum_{k=1}^{\infty} \dfrac{\sigma_n(k)}{k^z} = \zeta(z) \zeta(z-n),$$ where $\sigma_...")
- 22:16, 25 June 2016 (diff | hist) . . (+2) . . Sum of divisors
- 22:14, 25 June 2016 (diff | hist) . . (+222) . . Sum of divisors
- 22:12, 25 June 2016 (diff | hist) . . (+44) . . Constant multiple rule for derivatives
- 22:08, 25 June 2016 (diff | hist) . . (+87) . . Jacobi theta 3
- 22:08, 25 June 2016 (diff | hist) . . (+87) . . Jacobi theta 2
- 22:07, 25 June 2016 (diff | hist) . . (+87) . . Jacobi theta 1
- 22:07, 25 June 2016 (diff | hist) . . (+87) . . Jacobi theta 4
- 22:03, 25 June 2016 (diff | hist) . . (+476) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 22:01, 25 June 2016 (diff | hist) . . (-74) . . Jacobi theta 1 (→Properties)
- 22:00, 25 June 2016 (diff | hist) . . (+446) . . Jacobi theta 4
- 22:00, 25 June 2016 (diff | hist) . . (+446) . . Jacobi theta 3
- 22:00, 25 June 2016 (diff | hist) . . (+446) . . Jacobi theta 2
- 22:00, 25 June 2016 (diff | hist) . . (+402) . . Jacobi theta 1
- 21:58, 25 June 2016 (diff | hist) . . (+44) . . Jacobi theta 1
- 21:57, 25 June 2016 (diff | hist) . . (+595) . . N Derivative of Jacobi theta 1 at 0 (Created page with "==Theorem== The following formula holds: $$\vartheta_1'(0,q)=\vartheta_2(0,q) \vartheta_3(0,q) \vartheta_4(0,q),$$ where $\vartheta_1$ denotes the Jacobi theta 1, $\varthe...")
- 21:56, 25 June 2016 (diff | hist) . . (+33) . . Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3
- 21:55, 25 June 2016 (diff | hist) . . (+507) . . N Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3 (Created page with "==Theorem== The following formula holds: $$\vartheta_2^4(0,q)+\vartheta_4^4(0,q)=\vartheta_3^4(0,q),$$ where $\vartheta_2$ denotes the Jacobi theta 2, $\vartheta_4$ denote...")
- 21:53, 25 June 2016 (diff | hist) . . (+652) . . N Squares of theta relation for Jacobi theta 4 and Jacobi theta 4 (Created page with "==Theorem== The following formula holds: $$\vartheta_4^2(z,q)\vartheta_4^2(0,q)=\vartheta_3^2(z,q)\vartheta_3^2(0,q)-\vartheta_2^2(z,q)\vartheta_2^2(0,q),$$ where $\vartheta_4...")
- 21:51, 25 June 2016 (diff | hist) . . (+63) . . Squares of theta relation for Jacobi theta 3 and Jacobi theta 4
- 21:49, 25 June 2016 (diff | hist) . . (+599) . . N Squares of theta relation for Jacobi theta 3 and Jacobi theta 4 (Created page with "==Theorem== The following formula holds: $$\vartheta_3^2(z,q)\vartheta_4^2(0,q)=\vartheta_4^2(z,q)\vartheta_3^2(0,q)-\vartheta_1^2(z,q)\vartheta_2^2(0,q),$$ where $\vartheta_3...")
- 21:47, 25 June 2016 (diff | hist) . . (+63) . . Squares of theta relation for Jacobi theta 2 and Jacobi theta 4
- 21:47, 25 June 2016 (diff | hist) . . (-187) . . Squares of theta relation for Jacobi theta 2 and Jacobi theta 4
- 21:46, 25 June 2016 (diff | hist) . . (+786) . . N Squares of theta relation for Jacobi theta 2 and Jacobi theta 4 (Created page with "==Theorem== The following formula holds: $$\vartheta_2^2(z,q)\vartheta_4^2(0,q)=\vartheta_4^2(z,q)\vartheta_2^2(0,q)-\vartheta_1^2(z,q)\vartheta_3^2(0,q),$$ where $\vartheta_1...")
- 21:45, 25 June 2016 (diff | hist) . . (+63) . . Squares of theta relation for Jacobi theta 1 and Jacobi theta 4
- 21:44, 25 June 2016 (diff | hist) . . (+550) . . N Squares of theta relation for Jacobi theta 1 and Jacobi theta 4 (Created page with "==Theorem== The following formula holds: $$\vartheta_1^2(z,q)\vartheta_4^2(0,q)=\vartheta_3^2(z,q)\vartheta_2^2(0,q)-\vartheta_2^2(z,q)\vartheta_3^2(0,q),$$ where $\vartheta_1...")
- 21:42, 25 June 2016 (diff | hist) . . (+57) . . Jacobi theta 4
- 21:39, 25 June 2016 (diff | hist) . . (+120) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 21:38, 25 June 2016 (diff | hist) . . (+414) . . N Jacobi theta 4 (Created page with "Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_4$ function is defined by $$\vartheta_4(z,q)=1+2\displaystyle\sum_{k=1}^{\infty} (-1)^k q^{k^2} \cos(2kz),$$ where $...")
- 21:37, 25 June 2016 (diff | hist) . . (+37) . . Jacobi theta 2
- 21:36, 25 June 2016 (diff | hist) . . (+415) . . N Jacobi theta 3 (Created page with "Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_3$ function is defined by $$\vartheta_3(z,q)=1+2\displaystyle\sum_{k=1}^{\infty} q^{k^2} \cos(2kz),$$ where $\cos$ d...")
- 21:35, 25 June 2016 (diff | hist) . . (+8) . . Jacobi theta 2
- 21:34, 25 June 2016 (diff | hist) . . (+398) . . N Jacobi theta 2 (Created page with "__NOTOC__ The Jacobi $\vartheta_2$ function is defined by $$\vartheta_2(z,q)=2q^{\frac{1}{4}}\displaystyle\sum_{k=0}^{\infty} q^{k(k+1)} \cos(2k+1)z,$$ where $\cos$ denotes th...")
- 21:32, 25 June 2016 (diff | hist) . . (+441) . . N Jacobi theta 1 (Created page with "__NOTOC__ Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_1$ function is defined by $$\vartheta_1(z,q)=2q^{\frac{1}{4}} \displaystyle\sum_{k=0}^{\infty} (-1)^k q^{k...")
- 21:21, 25 June 2016 (diff | hist) . . (+100) . . Main Page (→Special functions)
- 13:19, 25 June 2016 (diff | hist) . . (+44) . . Relationship between Weber function 1 and Struve function 1 (current)
- 13:18, 25 June 2016 (diff | hist) . . (+44) . . Relationship between Weber function 0 and Struve function 0 (current)
- 13:18, 25 June 2016 (diff | hist) . . (-161) . . Relationship between Struve function and hypergeometric pFq (current)
- 13:18, 25 June 2016 (diff | hist) . . (-612) . . Struve function
- 13:17, 25 June 2016 (diff | hist) . . (+15) . . Struve function
- 06:16, 25 June 2016 (diff | hist) . . (+3,325) . . Book:Harris Hancock/Lectures on the theory of elliptic functions (current)
- 05:25, 25 June 2016 (diff | hist) . . (+15,170) . . Book:Harris Hancock/Lectures on the theory of elliptic functions
- 03:51, 25 June 2016 (diff | hist) . . (+3,180) . . N Book:Harris Hancock/Lectures on the theory of elliptic functions (Created page with "{{Book|Lectures on the theory of elliptic functions|1910|||Harris Hancock}} ===Online copies=== [https://archive.org/details/lecturestheorell00hancrich hosted by archive.org]...")
- 01:05, 25 June 2016 (diff | hist) . . (-120) . . Relationship between q-derivative and derivative (current)
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