Transformations

Transformations and argument simplifications

Argument involving basic arithmetic operations

Involving sin^-1(- z)

Involving sin^-1(-z) and sin^-1(z)

Involving sin^-1((z₂)^1/2)

Involving sin^-1((z₂)^1/2) and sin^-1(z)

Involving sin^-1(a (b z^c)^m)

Involving sin^-1(a (b z^c)^m) and sin^-1(a b^m z^{m c})

Involving sin^-1(1-2z²)

Involving sin^-1(1-2 z²) and sin^-1(z)

Involving sin^-1(2 z²-1)

Involving sin^-1(2 z²-1) and sin^-1(z)

Involving sin^-1(z²-2/z²)

Involving sin^-1(z²-2/z²) and sin^-1(1/z)

Involving sin^-1(2-z²/z²)

Involving sin^-1(2-z²/z²) and sin^-1(1/z)

Involving sin^-1((1-z)^1/2)

Involving sin^-1((1-z)^1/2) and sin^-1(z^1/2)

Involving sin ^-1(1+c z/2^1/2)

Involving sin^-1(1+z/2^1/2) and sin^-1(z)

Involving sin^-1(1-z/2^1/2) and sin^-1(z)

Involving sin^-1((z-1)^1/2/z^1/2)

Involving sin^-1((z-1)^1/2/z^1/2) and sin^-1(1/z^1/2)

Involving sin^-1((z-1)^1/2/z^1/2) and sin^-1(1/z^1/2)

Involving sin^-1((1-z)^1/2/(-z)^1/2)

Involving sin^-1((1-z)^1/2/(-z)^1/2) and sin^-1(1/z^1/2)

Involving sin^-1((1-z)^1/2/(-z)^1/2) and sin^-1(1/z^1/2)

Involving sin^-1(z-1/z^1/2)

Involving sin^-1(z-1/z^1/2) and sin^-1(1/z^1/2)

Involving sin^-1(z-1/z^1/2) and sin^-1(1/z^1/2)

Involving sin^-1((z+a)^1/2/(2 z)^1/2)

Involving sin^-1((z-1)^1/2/(2 z)^1/2) and sin^-1(1/z)

Involving sin^-1((z+1)^1/2/(2 z)^1/2) and sin^-1(1/z)

Involving sin^-1((a-z)^1/2/(-2 z)^1/2)

Involving sin^-1((1-z)^1/2/(-2 z)^1/2) and sin^-1(1/z)

Involving sin^-1((-z-1)^1/2/(-2 z)^1/2) and sin^-1(1/z)

Involving sin^-1(z+a/2 z^1/2)

Involving sin^-1(z-1/2 z^1/2) and sin^-1(1/z)

Involving sin^-1(z+1/2 z^1/2) and sin^-1(1/z)

Involving sin^-1((1-z²)^1/2)

Involving sin^-1((1-z²)^1/2) and sin^-1(z)

Involving sin^-1((z²-1)^1/2/z)

Involving sin^-1((z²-1)^1/2/z) and sin^-1(1/z)

Involving sin^-1((z²-1)^1/2/(z₂)^1/2)

Involving sin^-1((z²-1)^1/2/(z₂)^1/2) and sin^-1(1/z)

Involving sin^-1((1-z²)^1/2/(-z²)^1/2)

Involving sin^-1((1-z²)^1/2/(-z²)^1/2) and sin^-1(1/z)

Involving sin^-1(z²-1/z^21/2)

Involving sin^-1(z²-1/z^21/2) and sin^-1(1/z)

Involving sin^-1(2 z (1-z²)^1/2)

Involving sin^-1(2 z (1-z²)^1/2) and sin^-1(z)

Involving sin^-1(2 (z²-1)^1/2/z²)

Involving sin^-1(2 (z²-1)^1/2/z²) and sin^-1(1/z)

Involving sin^-1(((1-(1+c z²)^1/2)/2)^1/2)

Involving sin^-1(((1-(1+z²)^1/2)/2 )^1/2) and sin^-1(i z)

Involving sin^-1(((1-(1-z²)^1/2)/2 )^1/2) and sin^-1(z)

Involving sin^-1(z (1-(1-z²)^1/2)^1/2/(2z²)^1/2)

Involving sin^-1(z (1-(1-z²)^1/2)^1/2/(2z²)^1/2) and sin^-1(z)

Involving sin^-1(z ((1-(1-z²)^1/2)/(2z²))^1/2)

Involving sin^-1(z ((1-(1-z²)^1/2)/(2z²))^1/2) and sin^-1(z)

Involving sin^-1((z-(z²-1)^1/2)^1/2/(2z)^1/2)

Involving sin^-1((z-(z²-1)^1/2)^1/2/(2z)^1/2) and sin^-1(1/z)

Involving sin^-1(((z-(z²-1)^1/2)/(2z))^1/2)

Involving sin^-1((z-(z²-1)^1/2)^1/2/(2z)) and sin^-1(1/z)

Involving sin^-1(c z^-r (-1+z^{2 r}/c²)^1/2)

Involving sin^-1(c z^-r (-1+z^{2 r}/c²)^1/2) and sin^-1(c/z^r)

Products, sums, and powers of the direct function

Sums of the direct function

Differences of the direct function

Linear combinations of the direct function

Related transformations

Sums involving the direct function

Involving log(z)

Involving cos^-1(z)

Involving tan^-1(z)

Involving cot^-1(z)

Involving csc^-1(z)

Involving sec^-1(z)

Involving sinh^-1(z)

Involving cosh^-1(z)

Involving tanh^-1(z)

Involving coth^-1(z)

Involving csch^-1(z)

Involving sech^-1(z)

Differences involving the direct function

Involving log(z)

Involving cos^-1(z)

Involving tan^-1(z)

Involving cot^-1(z)

Involving csc^-1(z)

Involving sec^-1(z)

Involving sinh^-1(z)

Involving cosh^-1(z)

Involving tanh^-1(z)

Involving coth^-1(z)

Involving csch^-1(z)

Involving sech^-1(z)

Linear combinations involving the direct function

Involving log(z)

Involving cos^-1(z)

Involving tan^-1(z)

Involving cot^-1(z)

Involving csc^-1(z)

Involving sec^-1(z)

Involving sinh^-1(z)

Involving cosh^-1(z)

Involving tanh^-1(z)

Involving coth^-1(z)

Involving csch^-1(z)

Involving sech^-1(z)