User contributions
(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)
- 02:53, 25 June 2017 (diff | hist) . . (0) . . Relationship between dilogarithm and log(1-z)/z
- 02:53, 25 June 2017 (diff | hist) . . (+32) . . N L 2(z)=zPhi(z,2,1) (Tom moved page L 2(z)=zPhi(z,2,1) to Li2(z)=zPhi(z,2,1)) (current)
- 02:53, 25 June 2017 (diff | hist) . . (0) . . m Li2(z)=zPhi(z,2,1) (Tom moved page L 2(z)=zPhi(z,2,1) to Li2(z)=zPhi(z,2,1))
- 02:52, 25 June 2017 (diff | hist) . . (+400) . . N Li2(z)=zPhi(z,2,1) (Created page with "==Theorem== The following formula holds: $$\mathrm{Li}_2(z)=z\Phi(z,2,1),$$ where $\mathrm{Li}_2$ denotes the dilogarithm and $\Phi$ denotes the Lerch transcendent. =...")
- 02:51, 25 June 2017 (diff | hist) . . (+139) . . Relationship between dilogarithm and log(1-z)/z
- 02:50, 25 June 2017 (diff | hist) . . (+163) . . Dilogarithm
- 02:47, 25 June 2017 (diff | hist) . . (+31) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 02:46, 25 June 2017 (diff | hist) . . (+198) . . Lerch transcendent
- 02:41, 25 June 2017 (diff | hist) . . (0) . . Clausen cosine
- 02:41, 25 June 2017 (diff | hist) . . (0) . . Clausen sine
- 00:50, 25 June 2017 (diff | hist) . . (-3) . . Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry (→Contents)
- 00:50, 25 June 2017 (diff | hist) . . (+60) . . Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry (→Contents)
- 00:43, 25 June 2017 (diff | hist) . . (+142) . . Error function (current)
- 00:42, 25 June 2017 (diff | hist) . . (+17) . . Sine integral (→References) (current)
- 00:42, 25 June 2017 (diff | hist) . . (+135) . . Sine integral
- 00:41, 25 June 2017 (diff | hist) . . (+75) . . Cosine integral
- 00:38, 25 June 2017 (diff | hist) . . (+73) . . Exponential integral Ei
- 00:35, 25 June 2017 (diff | hist) . . (+98) . . Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry
- 00:34, 25 June 2017 (diff | hist) . . (0) . . Gamma (→References)
- 00:33, 25 June 2017 (diff | hist) . . (+132) . . Gamma
- 00:33, 25 June 2017 (diff | hist) . . (-3) . . Beta (→References)
- 00:33, 25 June 2017 (diff | hist) . . (+136) . . Beta
- 00:10, 25 June 2017 (diff | hist) . . (+4) . . Reciprocal gamma written as an infinite product
- 00:06, 25 June 2017 (diff | hist) . . (+30) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 00:06, 25 June 2017 (diff | hist) . . (+194) . . Bernoulli numbers
- 00:02, 25 June 2017 (diff | hist) . . (+47) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
- 00:01, 25 June 2017 (diff | hist) . . (+987) . . Beta
- 23:58, 24 June 2017 (diff | hist) . . (+1,117) . . Book:Arthur Erdélyi/Higher Transcendental Functions Volume I (→Contents)
- 23:56, 24 June 2017 (diff | hist) . . (-12) . . Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y)
- 23:54, 24 June 2017 (diff | hist) . . (+181) . . Beta in terms of sine and cosine
- 23:53, 24 June 2017 (diff | hist) . . (+484) . . N Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y) (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(x)>0$ and $\mathrm{Re}(y)>0$: $$\displaystyle\int_{-1}^1 (1+t)^{2x-1}(1-t)^{2y-1}(1+t^2)^{-x-y} \mathrm{d}t= 2^{x+y-2}...")
- 23:51, 24 June 2017 (diff | hist) . . (+563) . . N Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) (Created page with "==Theorem== The following formula holds for $z>0$, $\mathrm{Re}(y)>0$, and $\mathrm{Re}(x)>0$: $$\displaystyle\int_0^1 t^{x-1} (1-t^z)^{y-1} \mathrm{d}t = \dfrac{1}{z} B \left...")
- 23:45, 24 June 2017 (diff | hist) . . (+635) . . N Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z) (Created page with "==Theorem== The following formula holds for $z>0$, $b>0$, and $0 < \mathrm{Re} \left( \dfrac{x+1}{z} \right) < \mathrm{Re}(y)$: $$\displaystyle\int_0^{\infty} (1+bt^z)^{-y} t^...")
- 23:22, 24 June 2017 (diff | hist) . . (0) . . Integral of (t-b)^(x-1)(a-t)^(y-1)/(c-t)^(x+y) dt = (a-b)^(x+y-1)/((c-a)^x (c-b)^y) B(x,y)
- 23:21, 24 June 2017 (diff | hist) . . (+606) . . N Integral of (t-b)^(x-1)(a-t)^(y-1)/(c-t)^(x+y) dt = (a-b)^(x+y-1)/((c-a)^x (c-b)^y) B(x,y) (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(x)>0$, $\mathrm{Re}(y)>0$, and $b<a<c$: $$\displaystyle\int_a^b \dfrac{(t-b)^{x-1}(a-t)^{y-1}}{(c-t)^{x+y}} \mathrm{d}...")
- 23:18, 24 June 2017 (diff | hist) . . (+84) . . Integral of (t-b)^(x-1)(a-t)^(y-1)/(t-x)^(x+y) dt=(a-b)^(x+y-1)/((a-c)^x(b-c)^y) B(x,y)
- 23:17, 24 June 2017 (diff | hist) . . (+505) . . N Integral of (t-b)^(x-1)(a-t)^(y-1)/(t-x)^(x+y) dt=(a-b)^(x+y-1)/((a-c)^x(b-c)^y) B(x,y) (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(x)>0$, $\mathrm{Re}(y) > 0$, and $c<b<a$: $$\displaystyle\int_a^b \dfrac{(t-b)^{x-1}(a-t)^{y-1}}{(t-c)^{x+y}} \mathrm{...")
- 23:15, 24 June 2017 (diff | hist) . . (+530) . . N Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(x)>0$, $\mathrm{Re}(y)>0$, and $b<a$: $$\displaystyle\int_a^b (t-b)^{x-1}(a-t)^{y-1} \mathrm{d}t=(a-b)^{x+y-1}B(x,y),$...")
- 23:13, 24 June 2017 (diff | hist) . . (+521) . . N Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) (Created page with "==Theorem== The following formula holds for $b>0$, $\mathrm{Re}(x)>0$, and $\mathrm{Re}(y)>0$: $$\displaystyle\int_0^{\infty} t^{-x-1} (1+bt)^{-x-y} \mathrm{d}t=b^{-x}B(x,y),$...")
- 23:11, 24 June 2017 (diff | hist) . . (+518) . . N Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) (Created page with "==Theorem== The following holds for $b>-1$, $\mathrm{Re}(x)>0$, and $\mathrm{Re}(y)>0$: $$\displaystyle\int_0^1 t^{x-1}(1-t)^{y-1}(1+bt)^{-x-y} \mathrm{d}t = (1+b)^{-x} B(x,y)...")
- 23:09, 24 June 2017 (diff | hist) . . (+504) . . N B(x,y)=2^(1-x-y)integral (1+t)^(x-1)(1-t)^(y-1)+(1+t)^(y-1)(1-t)^(x-1) dt (Created page with "==Theorem== The following formula holds for $\mathrm{Re}(x)>0$ and $\mathrm{Re}(y)>0$: $$B(x,y) = 2^{1-x-y} \displaystyle\int_0^1 (1+t)^{x-1}(1-t)^{y-1} + (1+t)^{y-1}(1-t)^{x-...")
- 23:06, 24 June 2017 (diff | hist) . . (+67) . . 1/B(n,m)=n((n+m-1) choose (m-1))
- 23:05, 24 June 2017 (diff | hist) . . (+412) . . N 1/B(n,m)=n((n+m-1) choose (m-1)) (Created page with "==Theorem== The following formula holds: $$\dfrac{1}{B(n,m)} = n {{n+m-1} \choose {m-1}},$$ where $B$ denotes the beta function and ${{n+m-1} \choose {m-1}}$ denotes a b...")
- 23:04, 24 June 2017 (diff | hist) . . (+478) . . N 1/B(n,m)=m((n+m-1) choose (n-1)) (Created page with "==Theorem== The following formula holds: $$\dfrac{1}{B(n,m)} = m {{n+m-1} \choose {n-1}},$$ where $B$ denotes the beta function and ${{n+m-1} \choose {n-1}}$ denotes a b...")
- 23:02, 24 June 2017 (diff | hist) . . (+455) . . N B(x,y)B(x+y,z)B(x+y+z,u)=Gamma(x)Gamma(y)Gamma(z)Gamma(u)/Gamma(x+y+z+u) (Created page with "==Theorem== The following formula holds: $$B(x,y)B(x+y,z)B(x+y+z,u)=\dfrac{\Gamma(x)\Gamma(y)\Gamma(z)\Gamma(u)}{\Gamma(x+y+z+u)},$$ where $B$ denotes the beta function an...")
- 23:01, 24 June 2017 (diff | hist) . . (+394) . . N B(x,y)B(x+y,z)=B(z,x)B(x+z,y) (Created page with "==Theorem== The following formula holds: $$B(x,y)B(x+y,z)=B(z,x)B(x+z,y),$$ where $B$ denotes the beta function. ==Proof== ==References== * {{BookReference|Higher Transc...")
- 22:59, 24 June 2017 (diff | hist) . . (+346) . . N B(x,y)B(x+y,z)=B(y,z)B(y+z,x) (Created page with "==Theorem== The following formula holds: $$B(x,y)B(x+y,z)=B(y,z)B(y+z,x),$$ where $B$ denotes the beta function. ==Proof== ==References== * {{BookReference|Higher Transc...")
- 22:58, 24 June 2017 (diff | hist) . . (+345) . . N B(x,y+1)=(y/(x+y))B(x,y) (Created page with "==Theorem== The following formula holds: $$B(x,y+1)=\dfrac{y}{x+y} B(x,y),$$ where $B$ denotes the beta function. ==Proof== ==References== * {{BookReference|Higher Trans...")
- 22:57, 24 June 2017 (diff | hist) . . (+352) . . N B(x,y+1)=(y/x)B(x+1,y) (Created page with "==Theorem== The following formula holds: $$B(x,y+1)=\dfrac{y}{x} B(x+1,y),$$ where $B$ denotes the beta function. ==Proof== ==References== * {{BookReference|Higher Trans...")
- 22:56, 24 June 2017 (diff | hist) . . (+16) . . Beta as product of gamma functions
(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)
