Pages that link to "Template:BookReference"
The following pages link to Template:BookReference:
View (previous 250 | next 250) (20 | 50 | 100 | 250 | 500)- Kelvin ber (transclusion) (← links)
- Kelvin bei (transclusion) (← links)
- Kelvin ker (transclusion) (← links)
- Kelvin kei (transclusion) (← links)
- Anger function (transclusion) (← links)
- Weber function (transclusion) (← links)
- Relationship between Weber function and Anger function (transclusion) (← links)
- Relationship between Anger function and Weber function (transclusion) (← links)
- Erfc (transclusion) (← links)
- Exponential integral Ei (transclusion) (← links)
- Relationship between sinh and sin (transclusion) (← links)
- Relationship between cosh and cos (transclusion) (← links)
- Relationship between tanh and tan (transclusion) (← links)
- Relationship between coth and cot (transclusion) (← links)
- Euler product for Riemann zeta (transclusion) (← links)
- Q-exponential E sub 1/q (transclusion) (← links)
- Product rule for derivatives (transclusion) (← links)
- Darboux function (transclusion) (← links)
- Schwarz function (transclusion) (← links)
- Derivative of the exponential function (transclusion) (← links)
- Pythagorean identity for sinh and cosh (transclusion) (← links)
- Gamma(1)=1 (transclusion) (← links)
- Gamma(z+1)=zGamma(z) (transclusion) (← links)
- Gamma(n+1)=n! (transclusion) (← links)
- Taylor series for error function (transclusion) (← links)
- Error function is odd (transclusion) (← links)
- Integral representation of polygamma for Re(z) greater than 0 (transclusion) (← links)
- Polygamma recurrence relation (transclusion) (← links)
- Polygamma reflection formula (transclusion) (← links)
- Book:Andrew Gray/A Treatise on Bessel Functions (transclusion) (← links)
- Template:BookReference (transclusion) (← links)
- Taylor series of log(1-z) (transclusion) (← links)
- Relationship between dilogarithm and log(1-z)/z (transclusion) (← links)
- Derivative of Li 2(-1/x) (transclusion) (← links)
- Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x) (transclusion) (← links)
- Relationship between Li 2(1),Li 2(-1), and pi (transclusion) (← links)
- Li 2(1)=pi^2/6 (transclusion) (← links)
- Binomial theorem (transclusion) (← links)
- Binomial coefficient (n choose k) equals (n choose (n-k)) (transclusion) (← links)
- Binomial coefficient (n choose k) equals (-1)^k ((k-n-1) choose k) (transclusion) (← links)
- Binomial coefficient ((n+1) choose k) equals (n choose k) + (n choose (k-1)) (transclusion) (← links)
- Binomial coefficient (n choose 0) equals 1 (transclusion) (← links)
- Binomial coefficient (n choose n) equals 1 (transclusion) (← links)
- Sum over bottom of binomial coefficient with top fixed equals 2^n (transclusion) (← links)
- Alternating sum over bottom of binomial coefficient with top fixed equals 0 (transclusion) (← links)
- Sum rule for derivatives (transclusion) (← links)
- Constant multiple rule for derivatives (transclusion) (← links)
- Quotient rule for derivatives (transclusion) (← links)
- Chain rule for derivatives (transclusion) (← links)
- Real and imaginary parts of log (transclusion) (← links)
- Polar coordinates (transclusion) (← links)
- Logarithm (multivalued) (transclusion) (← links)
- Relationship between logarithm (multivalued) and logarithm (transclusion) (← links)
- Logarithm (multivalued) of product is a sum of logarithms (multivalued) (transclusion) (← links)
- Logarithm of product is a sum of logarithms (transclusion) (← links)
- Logarithm (multivalued) of a quotient is a difference of logarithms (multivalued) (transclusion) (← links)
- Logarithm of a quotient is a difference of logarithms (transclusion) (← links)
- Relationship between logarithm (multivalued) and positive integer exponents (transclusion) (← links)
- Relationship between logarithm and positive integer exponents (transclusion) (← links)
- Logarithm of 1 (transclusion) (← links)
- Logarithm diverges to negative infinity at 0 from right (transclusion) (← links)
- Logarithm at minus 1 (transclusion) (← links)
- Logarithm at i (transclusion) (← links)
- Logarithm at -i (transclusion) (← links)
- E is limit of (1+1/n)^n (transclusion) (← links)
- Taylor series of log(1+z) (transclusion) (← links)
- Series for log(z) for Re(z) greater than 1/2 (transclusion) (← links)
- Series for log(z) for absolute value of (z-1) less than 1 (transclusion) (← links)
- Series for log(z) for Re(z) greater than 0 (transclusion) (← links)
- Laurent series for log((z+1)/(z-1)) for absolute value of z greater than 1 (transclusion) (← links)
- Series for log(z+a) for positive a and Re(z) greater than -a (transclusion) (← links)
- Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0 (transclusion) (← links)
- Gamma function written as a limit of a factorial, exponential, and a rising factorial (transclusion) (← links)
- Gamma function written as infinite product (transclusion) (← links)
- Reciprocal gamma written as an infinite product (transclusion) (← links)
- Erf of conjugate is conjugate of erf (transclusion) (← links)
- Two-sided inequality for e^(x^2) integral from x to infinity e^(-t^2) dt for non-negative real x (transclusion) (← links)
- Continued fraction for 2e^(z^2) integral from z to infinity e^(-t^2) dt for positive Re(z) (transclusion) (← links)
- Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt (transclusion) (← links)
- Limit of erf when z approaches infinity and the modulus of arg(z) is less than pi/4 (transclusion) (← links)
- 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)