9 Trigonometric/polynomial equations and the algebraic nature of trig functions 7 Functions that are easy to antidifferentiate but whose inverses are hard to antidifferentiate 6 Express solutions of equation $\tan x= x$ in closed form 5 How do we know if a function has an elementary inverse? 5 Why is it that the Lambert W relation cannot be expressed in terms of elementary functions?

### Reputation (3,565)

 +10 Equations solvable by Lambert Function +10 closed-form expression for roots of a polynomial +10 Polynomial equals exponential? +10 Can we list explicitly all types of polynomial equations of one unknown that are solvable by radicals?

### Questions (38)

 5 The conjecture about the existence of closed-form inverses of functions 5 What is the inverse of simply composited elementary functions? 4 What are the general formulas for the transformations of the periods of the Weierstrass elliptic functions $\wp$? 3 Can each root equation be rearranged to a corresponding polynomial equation? 3 Explain Application of Risch's Structure Theorem for Elementary Functions

### Tags (129)

 55 closed-form × 41 22 trigonometry × 8 53 calculus × 47 21 combinatorics × 21 40 algebra-precalculus × 37 20 transcendental-equations × 11 33 elementary-functions × 28 18 reference-request × 14 28 integration × 24 17 functions × 17

### Bookmarks (13)

 6 Proving that special functions do not have closed-form expression 6 Integrability of a polynomial under root 4 How can I solve $\int \frac{P_1(t)}{P_2(t)e^{P_3(t)}} dt$ 3 Explain Application of Risch's Structure Theorem for Elementary Functions 3 Why some inverse functions do not have a closed form