Pages that link to "Template:BookReference"
The following pages link to Template:BookReference:
View (previous 500 | next 500) (20 | 50 | 100 | 250 | 500)- Anger of integer order is Bessel J (transclusion) (← links)
- Versine (transclusion) (← links)
- Coversine (transclusion) (← links)
- Haversine (transclusion) (← links)
- Exsecant (transclusion) (← links)
- Logarithm (multivalued) of the exponential (transclusion) (← links)
- Logarithm of exponential (transclusion) (← links)
- Exponential of logarithm (transclusion) (← links)
- E^(-x/(1-x)) is less than 1-x is less than e^(-x) for nonzero real x less than 1 (transclusion) (← links)
- E^x is greater than 1+x for nonzero real x (transclusion) (← links)
- E^x is less than 1/(1-x) for nonzero real x less than 1 (transclusion) (← links)
- X/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1 (transclusion) (← links)
- X less than e^x-1 less than x/(1-x) for nonzero real x less than 1 (transclusion) (← links)
- 1+x greater than exp(x/(1+x)) for nonzero real x greater than -1 (transclusion) (← links)
- E^x greater than 1+x^n/n! for n greater than 0 and nonzero real x greater than 0 (transclusion) (← links)
- E^x greater than (1+x/y)^y greater than exp(xy/(x+y) for x greater than 0 and y greater than 0) (transclusion) (← links)
- E^(-x) less than 1-(x/2) for 0 less than x less than or equal to 1.5936 (transclusion) (← links)
- Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1 (transclusion) (← links)
- Abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z)) (transclusion) (← links)
- Gauss' formula for gamma function (transclusion) (← links)
- Differential equation for Jacobi P (transclusion) (← links)
- Hankel H (1) in terms of csc and Bessel J (transclusion) (← links)
- Hankel H (2) in terms of csc and Bessel J (transclusion) (← links)
- Relationship between Bessel J sub n and Bessel J sub -n (transclusion) (← links)
- Relationship between Bessel Y sub n and Bessel Y sub -n (transclusion) (← links)
- Value of polygamma at 1 (transclusion) (← links)
- Value of polygamma at positive integer (transclusion) (← links)
- Value of polygamma at 1/2 (transclusion) (← links)
- Value of derivative of trigamma at positive integer plus 1/2 (transclusion) (← links)
- Polygamma multiplication formula (transclusion) (← links)
- Gamma recurrence relation (transclusion) (← links)
- Template:PaperReference (transclusion) (← links)
- Q-number when a=n is a natural number (transclusion) (← links)
- Meromorphic continuation of q-exponential E sub q (transclusion) (← links)
- Q-difference equation for q-exponential E sub q (transclusion) (← links)
- Q-difference equation for q-exponential E sub 1/q (transclusion) (← links)
- Derivative of Bessel J with respect to its order (transclusion) (← links)
- Derivative of Bessel Y with respect to its order (transclusion) (← links)
- Product representation of q-exponential E sub 1/q (transclusion) (← links)
- Limit of q-exponential E sub 1/q for 0 less than q less than 1 (transclusion) (← links)
- Relationship between csch and csc (transclusion) (← links)
- Relationship between sech and sec (transclusion) (← links)
- Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1 (transclusion) (← links)
- Identity written as a sum of Möbius functions (transclusion) (← links)
- Möbius function is multiplicative (transclusion) (← links)
- Generating relation for Bateman F (transclusion) (← links)
- Three-term recurrence for Bateman F (transclusion) (← links)
- Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2 (transclusion) (← links)
- Sum of totient equals z/((1-z) squared) (transclusion) (← links)
- Product representation of totient (transclusion) (← links)
- Euler totient is multiplicative (transclusion) (← links)
- Beta as improper integral (transclusion) (← links)
- Beta is symmetric (transclusion) (← links)
- Beta as product of gamma functions (transclusion) (← links)
- Digamma functional equation (transclusion) (← links)
- Digamma at n+1 (transclusion) (← links)
- Digamma at 1 (transclusion) (← links)
- Digamma at z+n (transclusion) (← links)
- Jacobi theta 1 (transclusion) (← links)
- Jacobi theta 2 (transclusion) (← links)
- Jacobi theta 3 (transclusion) (← links)
- Jacobi theta 4 (transclusion) (← links)
- Squares of theta relation for Jacobi theta 1 and Jacobi theta 4 (transclusion) (← links)
- Squares of theta relation for Jacobi theta 2 and Jacobi theta 4 (transclusion) (← links)
- Squares of theta relation for Jacobi theta 3 and Jacobi theta 4 (transclusion) (← links)
- Squares of theta relation for Jacobi theta 4 and Jacobi theta 4 (transclusion) (← links)
- Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3 (transclusion) (← links)
- Derivative of Jacobi theta 1 at 0 (transclusion) (← links)
- Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1 (transclusion) (← links)
- Generating function for partition function (transclusion) (← links)
- Closed form for partition function with sinh (transclusion) (← links)
- Pure recurrence relation for partition function (transclusion) (← links)
- Recurrence relation for partition function with sum of divisors (transclusion) (← links)
- Sum of divisors functions written in terms of partition function (transclusion) (← links)
- Asymptotic formula for partition function (transclusion) (← links)
- Hypergeometric 2F1 (transclusion) (← links)
- Limit of (1/Gamma(c))*2F1(a,b;c;z) as c approaches -m (transclusion) (← links)
- 2F1(1,1;2;z)=-log(1-z)/z (transclusion) (← links)
- 2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z) (transclusion) (← links)
- 2F1(1/2,1;3/2;-z^2)=arctan(z)/z (transclusion) (← links)
- 2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z (transclusion) (← links)
- Q-derivative of q-Cosine (transclusion) (← links)
- Q-derivative of q-Sine (transclusion) (← links)
- Logarithmic derivative of Jacobi theta 1 equals cotangent + a sum of sines (transclusion) (← links)
- Logarithmic derivative of Jacobi theta 2 equals negative tangent + a sum of sines (transclusion) (← links)
- Logarithmic derivative of Jacobi theta 3 equals a sum of sines (transclusion) (← links)
- Logarithmic derivative of Jacobi theta 4 equals a sum of sines (transclusion) (← links)
- Logarithm of quotient of Jacobi theta 1 equals the log of a quotient of sines + a sum of sines (transclusion) (← links)
- Logarithm of quotient of Jacobi theta 2 equals the log of a quotient of cosines + a sum of sines (transclusion) (← links)
- Logarithm of quotient of Jacobi theta 3 equals a sum of sines (transclusion) (← links)
- Logarithm of a quotient of Jacobi theta 4 equals a sum of sines (transclusion) (← links)
- Integral of monomial times Bessel J (transclusion) (← links)
- Integral of Bessel J for Re(nu) greater than -1 (transclusion) (← links)
- Integral of Bessel J for nu=2n (transclusion) (← links)
- Integral of Bessel J for nu=2n+1 (transclusion) (← links)
- Integral of Bessel J for nu=n+1 (transclusion) (← links)
- Integral of Bessel J for nu=1 (transclusion) (← links)
- Series for log(riemann zeta) over primes (transclusion) (← links)
- Series for log(Riemann zeta) in terms of Mangoldt function (transclusion) (← links)
- Logarithmic derivative of Riemann zeta in terms of series over primes (transclusion) (← links)
- Logarithmic derivative of Riemann zeta in terms of Mangoldt function (transclusion) (← links)
- Generating function for Hermite (physicist) polynomials (transclusion) (← links)
- Closed formula for physicist's Hermite polynomials (transclusion) (← links)
- Hermite (physicist) polynomial at negative argument (transclusion) (← links)
- Series for q-sin sub q (transclusion) (← links)
- Sqrt(1-z^2)2F1(1,1;3/2;z^2)=arcsin(z)/z (transclusion) (← links)
- Period of sinh (transclusion) (← links)
- Period of cosh (transclusion) (← links)
- Period of tanh (transclusion) (← links)
- Symmetry relation of exponential integral E (transclusion) (← links)
- Recurrence relation of exponential integral E (transclusion) (← links)
- Digamma at 1/2 (transclusion) (← links)
- Digamma at n+1/2 (transclusion) (← links)
- (c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0 (transclusion) (← links)
- (b-a)2F1+a2F1(a+1)-b2F1(b+1)=0 (transclusion) (← links)
- (c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0 (transclusion) (← links)
- C(a-(c-b)z)2F1-ac(1-z)2F1(a+1)+(c-a)(c-b)z2F1(c+1)=0 (transclusion) (← links)
- (c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0 (transclusion) (← links)
- (c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0 (transclusion) (← links)
- Reciprocal Riemann zeta in terms of Mobius (transclusion) (← links)
- Derivative of the logarithm (transclusion) (← links)
- Beta in terms of power of t over power of (1+t) (transclusion) (← links)
- Riemann zeta as integral of monomial divided by an exponential (transclusion) (← links)
- Q-number of a negative (transclusion) (← links)
- 1/q-number as a q-number (transclusion) (← links)
- Q-shifted factorial (transclusion) (← links)
- Asymptotic behavior of Sievert integral (transclusion) (← links)
- Relationship between Sievert integral and exponential integral E (transclusion) (← links)
- Series for polygamma in terms of Riemann zeta (transclusion) (← links)
- Dirichlet series (transclusion) (← links)
- General Dirichlet series (transclusion) (← links)
- Riemann zeta as contour integral (transclusion) (← links)
- Riemann zeta at even integers (transclusion) (← links)
- Functional equation for Riemann zeta (transclusion) (← links)
- Functional equation for Riemann zeta with cosine (transclusion) (← links)
- Functional equation for Riemann xi (transclusion) (← links)
- Riemann-Landau xi (transclusion) (← links)
- Riemann-Landau xi is even (transclusion) (← links)
- Pochhammer symbol with non-negative integer subscript (transclusion) (← links)
- 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z) (transclusion) (← links)
- 0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z) (transclusion) (← links)
- 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4) (transclusion) (← links)
- 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) (transclusion) (← links)
- 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4) (transclusion) (← links)
- 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) (transclusion) (← links)
- 1Phi0(a;;z) as infinite product (transclusion) (← links)
- 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z) (transclusion) (← links)
- (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k) (transclusion) (← links)
- 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k) (transclusion) (← links)
- Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) (transclusion) (← links)
- B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt (transclusion) (← links)
- B(x,y+1)=(y/x)B(x+1,y) (transclusion) (← links)
- B(x,y+1)=(y/(x+y))B(x,y) (transclusion) (← links)
- B(x,y)B(x+y,z)=B(y,z)B(y+z,x) (transclusion) (← links)
- B(x,y)B(x+y,z)=B(z,x)B(x+z,y) (transclusion) (← links)
- 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) (transclusion) (← links)
- 1/B(n,m)=m((n+m-1) choose (n-1)) (transclusion) (← links)
- 1/B(n,m)=n((n+m-1) choose (m-1)) (transclusion) (← links)
- 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 (transclusion) (← links)
- Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) (transclusion) (← links)
- Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) (transclusion) (← links)
- Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) (transclusion) (← links)
- 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) (transclusion) (← links)
- 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) (transclusion) (← links)
- Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z) (transclusion) (← links)
- Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) (transclusion) (← links)
- Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y) (transclusion) (← links)
- Li2(z)=zPhi(z,2,1) (transclusion) (← links)
- Logarithm base a (transclusion) (← links)
- Log base a in terms of logarithm base b (transclusion) (← links)
- Log a(b)=1/log b(a) (transclusion) (← links)
- Log e(z)=log(z) (transclusion) (← links)
- Log 10(z)=log(z)/log(10) (transclusion) (← links)
- Log 10(z)=log 10(e)log(z) (transclusion) (← links)
- Log(z)=log(10)log 10(z) (transclusion) (← links)
- Limit of log(x)/x^a=0 (transclusion) (← links)
- Limit of x^a log(x)=0 (transclusion) (← links)
- X/(1+x) less than log(1+x) (transclusion) (← links)
- Log(1+x) less than x (transclusion) (← links)
- X less than -log(1-x) (transclusion) (← links)
- -log(1-x) less than x/(1-x) (transclusion) (← links)
- Abs(log(1-x)) less than 3x/2 (transclusion) (← links)
- Log(x) less than or equal to x-1 (transclusion) (← links)
- Log(x) less than or equal to n(x^(1/n)-1) (transclusion) (← links)
- Abs(log(1+z)) less than or equal to -log(1-abs(z)) (transclusion) (← links)
- Log(1+z) as continued fraction (transclusion) (← links)
- Log((1+z)/(1-z)) as continued fraction (transclusion) (← links)
- Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 (transclusion) (← links)
- Two-dimensional Laplace transform (transclusion) (← links)
- Unit step function (transclusion) (← links)
- Pythagorean identity for tanh and sech (transclusion) (← links)
- Pythagorean identity for coth and csch (transclusion) (← links)
- Sum of cosh and sinh (transclusion) (← links)
- Difference of cosh and sinh (transclusion) (← links)
- Sinh is odd (transclusion) (← links)
- Cosh is even (transclusion) (← links)
- Tanh is odd (transclusion) (← links)
- Sinh of a sum (transclusion) (← links)
- Cosh of a sum (transclusion) (← links)
- Tanh of a sum (transclusion) (← links)
- Coth of a sum (transclusion) (← links)
- Halving identity for sinh (transclusion) (← links)
- Halving identity for cosh (transclusion) (← links)
- Halving identity for tangent (1) (transclusion) (← links)
- Halving identity for tangent (2) (transclusion) (← links)
- Halving identity for tangent (3) (transclusion) (← links)
- Doubling identity for sinh (1) (transclusion) (← links)
- Doubling identity for sinh (2) (transclusion) (← links)
- Doubling identity for cosh (1) (transclusion) (← links)
- Doubling identity for cosh (2) (transclusion) (← links)
- Doubling identity for cosh (3) (transclusion) (← links)
- Integral representation of Struve function (transclusion) (← links)
- Integral representation of Struve function (2) (transclusion) (← links)
- Integral representation of Struve function (3) (transclusion) (← links)
- Recurrence relation for Struve fuction (transclusion) (← links)
- Recurrence relation for Struve function (2) (transclusion) (← links)
- Derivative of Struve H0 (transclusion) (← links)
- 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t) (transclusion) (← links)
- Orthogonality relation for cosine on (0,pi) (transclusion) (← links)
- Orthogonality of Chebyshev T on (-1,1) (transclusion) (← links)
- Matrix exponential (transclusion) (← links)
- D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) (transclusion) (← links)
- D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1) (transclusion) (← links)
- H (nu)(x) geq 0 for x gt 0 and nu geq 1/2 (transclusion) (← links)
- H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0 (transclusion) (← links)
- H (1/2)(z)=sqrt(2/(pi z))(1-cos(z)) (transclusion) (← links)
- H (3/2)(z)=sqrt(z/(2pi))(1+2/z^2)-sqrt(2/(pi z))(sin(z)+cos(z)/z) (transclusion) (← links)
- Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z) (transclusion) (← links)
- K(m)=(pi/2)2F1(1/2,1/2;1;m) (transclusion) (← links)
- E(m)=(pi/2)2F1(-1/2,1/2;1;m) (transclusion) (← links)
- Nth derivative of logarithm (transclusion) (← links)
- Antiderivative of the logarithm (transclusion) (← links)
- Integral of (z^n)log(z)dz=(z^(n+1)/(n+1))log(z)-z^(n+1)/(n+1)^2 for integer n neq -1 (transclusion) (← links)
- Gamma'(z)/Gamma(z)=-gamma-1/z+Sum z/(k(z+k)) (transclusion) (← links)
- Matrix e^A=limit of (I+A/s)^s (transclusion) (← links)
- Euler numbers (transclusion) (← links)
- Euler E n'(x)=nE n-1(x) (transclusion) (← links)
- Z coth(z) = 2z/(e^(2z)-1) + z (transclusion) (← links)
- Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! (transclusion) (← links)
- Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n) (transclusion) (← links)
- Generating function for Laguerre L (transclusion) (← links)
- L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x)) (transclusion) (← links)
- L n(0)=1 (transclusion) (← links)
- L n'(0)=-n (transclusion) (← links)
- Orthogonality of Laguerre L (transclusion) (← links)
- (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) (transclusion) (← links)
- XL n'(x)=nL n(x)-n L (n-1)(x) (transclusion) (← links)
- L n'(x)=-Sum L k(x) (transclusion) (← links)
- T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n (transclusion) (← links)
- U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n (transclusion) (← links)
- T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k) (transclusion) (← links)
- U n(x)=Sum (-1)^k n!/((2k+1)!(n-2k-1)!)(1-x^2)^(k+1/2)x^(n-2k-1) (transclusion) (← links)
- Ei(x)=-Integral from -x to infinity of e^(-t)/t dt (transclusion) (← links)