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- 21:31, 26 June 2016 (diff | hist) . . (-61) . . Hypergeometric 2F1
- 21:31, 26 June 2016 (diff | hist) . . (-61) . . Arcsin
- 21:30, 26 June 2016 (diff | hist) . . (+440) . . Hypergeometric 2F1
- 21:30, 26 June 2016 (diff | hist) . . (-454) . . Hypergeometric pFq
- 21:30, 26 June 2016 (diff | hist) . . (+3,221) . . N Differential equation for Hypergeometric pFq (Created page with "=Differential equation= Define the derivative operator $\vartheta=t \dfrac{d}{dt}$.Then $$\vartheta t^k = t \dfrac{d}{dt} t^k = t(kt^{k-1})=kt^k.$$ <div class="toccolours mw...") (current)
- 21:30, 26 June 2016 (diff | hist) . . (-3,156) . . Hypergeometric pFq
- 21:29, 26 June 2016 (diff | hist) . . (+3,035) . . N Derivatives of Hypergeometric pFq (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Proposition:</strong> Suppose that ${}_pF_q$ converges. Then $$\dfrac{d^n}{dt^n} {}_pF_q(\vec...") (current)
- 21:29, 26 June 2016 (diff | hist) . . (-3,014) . . Hypergeometric pFq
- 21:28, 26 June 2016 (diff | hist) . . (+16) . . Convergence of Hypergeometric pFq
- 21:28, 26 June 2016 (diff | hist) . . (+2,078) . . N Convergence of Hypergeometric pFq (Created page with "=Convergence= If any of the $a_j$'s is a a nonpositive integer, then the series terminates and is a polynomial. If any of the $b_{\ell}$'s is a nonpositive integer, the serie...")
- 21:27, 26 June 2016 (diff | hist) . . (-2,027) . . Hypergeometric pFq
- 21:26, 26 June 2016 (diff | hist) . . (+560) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 21:23, 26 June 2016 (diff | hist) . . (+235) . . Hypergeometric 2F1
- 21:23, 26 June 2016 (diff | hist) . . (+470) . . N 2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z (Created page with "==Theorem== The following formula holds: $${}_2F_1 \left( \dfrac{1}{2}, \dfrac{1}{2}; \dfrac{3}{2}; z^2 \right) = \dfrac{\arcsin(z)}{z},$$ where ${}_2F_1$ denotes the hyperg...")
- 21:21, 26 June 2016 (diff | hist) . . (+32) . . 2F1(1/2,1;3/2;-z^2)=arctan(z)/z
- 21:20, 26 June 2016 (diff | hist) . . (+465) . . N 2F1(1/2,1;3/2;-z^2)=arctan(z)/z (Created page with "==Theorem== The following formula holds: $${}_2F_1 \left( \dfrac{1}{2}, 1; \dfrac{3}{2} ; -z^2 \right)=\dfrac{\arctan(z)}{z},$$ where ${}_2F_1$ denotes the hypergeometric 2F...")
- 21:18, 26 June 2016 (diff | hist) . . (+493) . . N 2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z) (Created page with "==Theorem== The following formula holds: $${}_2F_1 \left( \dfrac{1}{2}, 1 ; \dfrac{3}{2}; z^2 \right)= \dfrac{1}{2z} \log \left( \dfrac{1+z}{1-z} \right),$$ where ${}_2F_1$ de...")
- 21:17, 26 June 2016 (diff | hist) . . (+22) . . 2F1(1,1;2;z)=-log(1-z)/z
- 21:15, 26 June 2016 (diff | hist) . . (+18) . . 2F1(1,1;2;z)=-log(1-z)/z
- 21:15, 26 June 2016 (diff | hist) . . (+439) . . N 2F1(1,1;2;z)=-log(1-z)/z (Created page with "==Theorem== The following formula holds: $${}_2F_1 \left( 1,1 ; 2 ; z \right) = -\dfrac{\log(1-z)}{z},$$ where ${}_2F_1$ denotes the hypergeometric 2F1 and $\log$ denotes...")
- 21:13, 26 June 2016 (diff | hist) . . (+588) . . N Limit of (1/Gamma(c))*2F1(a,b;c;z) as c approaches -m (Created page with "==Theorem== The following formula holds: $$\displaystyle\lim_{c \rightarrow -m} \dfrac{1}{\Gamma(c)} {}_2F_1(a,b;c;z)= \dfrac{(a)_{m+1} (b)_{m+1}}{(m+1)!} z^{m+1} {}_2F_1 \lef...")
- 21:10, 26 June 2016 (diff | hist) . . (+10) . . Hypergeometric 2F1
- 21:09, 26 June 2016 (diff | hist) . . (+476) . . N Hypergeometric 2F1 (Created page with "The (Gauss) hypergeometric ${}_2F_1$ function (often written simply as $F$) is defined by the series $${}_2F_1(a,b;c;z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(a)_k (b)_k}{(c...")
- 21:05, 26 June 2016 (diff | hist) . . (+286) . . Main Page
- 20:52, 26 June 2016 (diff | hist) . . (+270) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 20:50, 26 June 2016 (diff | hist) . . (+75) . . Sum of divisors (current)
- 20:50, 26 June 2016 (diff | hist) . . (+367) . . Partition (current)
- 20:49, 26 June 2016 (diff | hist) . . (+529) . . N Asymptotic formula for partition function (Created page with "==Theorem== The following asymptotic formula holds: $$p(n) \sim \dfrac{1}{4n\sqrt{3}} \exp \left( \pi \sqrt{ \dfrac{2}{3} } \sqrt{n} \right),$$ where $p$ denotes the partiti...")
- 20:47, 26 June 2016 (diff | hist) . . (+35) . . Sum of divisors functions written in terms of partition function (current)
- 20:47, 26 June 2016 (diff | hist) . . (+569) . . N Sum of divisors functions written in terms of partition function (Created page with "==Theorem== The following formula holds: $$\sigma_1(n)=p(n)+\displaystyle\sum_{1 \leq \frac{3k^2 \pm k}{2} \leq n} (-1)^k\dfrac{3k^2 \pm k}{2} p \left(n - \dfrac{3k^2 \pm k}{2...")
- 20:43, 26 June 2016 (diff | hist) . . (+530) . . N Recurrence relation for partition function with sum of divisors (Created page with "==Theorem== The following formula holds: $$p(n)=\dfrac{1}{n}\displaystyle\sum_{k=1}^n \sigma_1(k) p(n-k),$$ where $p$ denotes the partition function and $\sigma_1$ denotes...") (current)
- 20:41, 26 June 2016 (diff | hist) . . (+57) . . Pure recurrence relation for partition function (current)
- 20:40, 26 June 2016 (diff | hist) . . (-73) . . Pure recurrence relation for partition function
- 20:40, 26 June 2016 (diff | hist) . . (-11) . . Pure recurrence relation for partition function
- 20:40, 26 June 2016 (diff | hist) . . (-8) . . Closed form for partition function with sinh (current)
- 20:39, 26 June 2016 (diff | hist) . . (0) . . m Pure recurrence relation for partition function (Tom moved page Recurrence relation for partition function to Pure recurrence relation for partition function)
- 20:39, 26 June 2016 (diff | hist) . . (+61) . . N Recurrence relation for partition function (Tom moved page Recurrence relation for partition function to Pure recurrence relation for partition function) (current)
- 20:38, 26 June 2016 (diff | hist) . . (-1) . . Closed form for partition function with sinh
- 20:37, 26 June 2016 (diff | hist) . . (+11) . . Pure recurrence relation for partition function
- 20:36, 26 June 2016 (diff | hist) . . (-113) . . Closed form for partition function with sinh
- 20:36, 26 June 2016 (diff | hist) . . (+13) . . Closed form for partition function with sinh
- 20:35, 26 June 2016 (diff | hist) . . (+10) . . Pure recurrence relation for partition function
- 20:34, 26 June 2016 (diff | hist) . . (+10) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 20:34, 26 June 2016 (diff | hist) . . (+10) . . Generating function for partition function (current)
- 20:34, 26 June 2016 (diff | hist) . . (0) . . m Closed form for partition function with sinh (Tom moved page Closed form for partition function to Closed form for partition function with sinh)
- 20:34, 26 June 2016 (diff | hist) . . (+58) . . N Closed form for partition function (Tom moved page Closed form for partition function to Closed form for partition function with sinh) (current)
- 20:33, 26 June 2016 (diff | hist) . . (+129) . . Closed form for partition function with sinh
- 20:32, 26 June 2016 (diff | hist) . . (+828) . . Closed form for partition function with sinh
- 20:18, 26 June 2016 (diff | hist) . . (+257) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 00:06, 26 June 2016 (diff | hist) . . (+587) . . N Pure recurrence relation for partition function (Created page with "==Theorem== The following formula holds: $$p(n)=\displaystyle\sum_{1 \leq \frac{3k^3 \pm k}{2} \leq n} (-1)^{k-1} p \left( n - \dfrac{3k^2 \pm k}{2} \right) = \dfrac{1}{n} \di...")
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