Legendre transformation
Schwarzian derivative
Schwarzian
inverse function
homogeneous function
derivative
antidifference
surjection
derivation
fixed point
even function
quasianalytic
monotone function
additive function
exponential
equibounded
subpower
symmetric function
semi-elasticity
invex
analytic function
pseudopolynomial
zero
Laplace transform
birational
odd function
quadratic
inverse
Taylor series
injection
covariant
Herbrand function
argument
impulse function
Weyl algebra
develop
function-evaluation routine
Gaussian function
periodic function
chain rule
Herbrandization
level set
partial derivative
lift
pole
subadditivity
partial
differentiation
divergence
indefinite integral
binary function
logarithmic derivative
Skolemization
product rule
permutation
Boas-Buck polynomial
precomposition
quasideterminant
partial function
contravariant functor
involution
contragredient
differentiate
composition algebra
monomorphism
kernel
pseudoconcave
linear operator
switch
composition
concave envelope
Jacobi identity
inverse trigonometric function
Lipschitz
unfold
defunctionalization
ordinary differential equation
preimage
epimorphism
modulo
resummation
Green's function
hyperinvariant
transformation
characteristic polynomial
monomorphisation
bent function
evectant
convolution
bidifferential
Lagrange polynomial
transcendental function
integral
Boolean derivative
orthogonalization
neofunctionalized

English words for 'Given a function f(x,y,z,...) which is concave up with respect to x (i.e., its second derivative with respect to x is greater than zero), an involutive procedure for replacing x with another variable, say p=∂f/∂x thus yielding another function, say F=F(p,y,z,...). This new function contains all of the information of the original f encoded, as it were, within it so that ∂F/∂p=x and applying a similar transformation to F yields the original f. The formula is: F(p,y,z,...)=p·x(p)-f(x(p),y,z,...) where x must be expressed as a function of p. (Note: The concave upwardness means that ∂f/∂x is monotonically increasing, which means that p as a function of x is invertible, so x should be expressible as a function of p.)'

As you may have noticed, above you will find words for "Given a function f(x,y,z,...) which is concave up with respect to x (i.e., its second derivative with respect to x is greater than zero), an involutive procedure for replacing x with another variable, say p=∂f/∂x thus yielding another function, say F=F(p,y,z,...). This new function contains all of the information of the original f encoded, as it were, within it so that ∂F/∂p=x and applying a similar transformation to F yields the original f. The formula is: F(p,y,z,...)=p·x(p)-f(x(p),y,z,...) where x must be expressed as a function of p. (Note: The concave upwardness means that ∂f/∂x is monotonically increasing, which means that p as a function of x is invertible, so x should be expressible as a function of p.)". Hover the mouse over the word you'd like to know more about to view its definition. Click search related words by phrase or description. to find a better fitting word. Finally, thanks to ChatGPT, the overall results have been greatly improved.

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