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Category:Unproven
From specialfunctionswiki
Pages in category "Unproven"
The following 45 pages are in this category, out of 495 total.
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- (b-a)2F1+a2F1(a+1)-b2F1(b+1)=0
- (c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0
- (c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0
- (c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0
- (c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0
- (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x)
- (n+2)C (n+2)^(lambda)(x)=2(lambda+n+1)xC (n+1)^(lambda)(x)-(2lambda+n)C n^(lambda)(x)
- (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x))
- (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k)
0
1
- 1+x greater than exp(x/(1+x)) for nonzero real x greater than -1
- 1/B(n,m)=m((n+m-1) choose (n-1))
- 1/B(n,m)=n((n+m-1) choose (m-1))
- 1/q-number as a q-number
- 1F1(a;2a;z)1F1(b;2b;-z)=2F3(a/2+b/2,a/2+b/2+1/2;a+1/2,b+1/2,a+b;z^2/4)
- 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4)
- 1Phi0(a;;z) as infinite product
- 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z)
2
- 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t)
- 2F0(a,b;;z)2F0(a,b;;-z)=4F1(a,b,a/2+b/2,a/2+b/2+1/2;a+b;4z^2)
- 2F1(1,1;2;z)=-log(1-z)/z
- 2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z
- 2F1(1/2,1;3/2;-z^2)=arctan(z)/z
- 2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z)
- 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z)
- 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k)
A
- Abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z))
- Abs(log(1+z)) less than or equal to -log(1-abs(z))
- Abs(log(1-x)) less than 3x/2
- Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1
- Absolute convergence of secant zeta function
- Airy zeta function at 2
- Alternating sum over bottom of binomial coefficient with top fixed equals 0
- Antiderivative of arccosh
- Antiderivative of arcsin
- Antiderivative of arcsinh
- Antiderivative of arctanh
- Antiderivative of cosine integral
- Antiderivative of hyperbolic cosecant
- Antiderivative of inverse error function
- Antiderivative of sech