0
A holomorphic function is a function that is differentiable at every point on its domain. In order for it to be differentiable, it needs to satisfy the Cauchy-Riemann equation properties, such that:
f(z) = u(x,y) + iv(x,y)
ux = vy
vx = -uy
If that is so, then f'(z) = ux + ivx
Otherwise, if a function doesn't satisfy these conditions, we say that it's not holomorphic. For instance:
f(z) = z̅
Test with the following properties:
ux = vy
vx = -uy
z̅ is written as u(x,y) - iv(x,y). Take the partial derivatives of u(x,y) and v(x,y). Then:
ux = -vy
vx = -(-uy) = uy
Since the conditions don't hold, that function is not holomorphic.
Add your answer:
Earn +20 pts
What is the parent function for the exponential function?
The parent function of the exponential function is ax
A function takes the exponential function's output and returns the exponential function's input?
A __________ function takes the exponential function's output and returns the exponential function's input.
Is the inverse of an exponential function the quadratic function?
No. The inverse of an exponential function is a logarithmic function.
What do you call the inverse function of the exponential function?
Logarithmic Function
What is function notation in math terms?
An equation where the left is the function of the right. f(x)=x+3 is function notation. The answer is a function of what x is. f(g(x))= the answer the inside function substituted in the outside function.
What has the author Katsutoshi Yamanoi written?
Katsutoshi Yamanoi has written: 'Holomorphic curves in Abelian varieties and intersections with higher codimensional subvarieties' 'On the truncated small function theorem in Nevanlinna theory'
What is a biholomorphism?
A biholomorphism is a bijective holomorphism whose inverse is also holomorphic.
What has the author T Suwa written?
T. Suwa has written: 'Indices of vector fields and residues of singular holomorphic foliations' -- subject(s): Holomorphic functions, Index theory (Mathematics), Vector fields
What has the author David E Barrett written?
David E. Barrett has written: 'Transverse symmetries and proper holomorphic maps'
What has the author Peter R Mercer written?
Peter R. Mercer has written: 'Holomorphic maps between convex domains in C r'
What has the author Kang-Tae Kim written?
Kang-Tae Kim has written: 'Robin functions for complex manifolds and applications' -- subject(s): Holomorphic functions, Complex manifolds
What has the author F Brackx written?
F. Brackx has written: 'Clifford analysis' -- subject(s): Clifford algebras, Harmonic functions, Holomorphic functions, Theory of distributions (Functional analysis)
What has the author S Coen written?
S. Coen has written: 'Una introduzione ai dominii di Riemann non ramificati n-dimensionali' -- subject(s): Holomorphic mappings, Riemann surfaces
A formula prewritten by excel is called?
Function
What is the parent function for the exponential function?
The parent function of the exponential function is ax
What function tests a specific condition in Excel?
The IF function is the main function to do it and you can also use other logical functions, like the AND function, the OR function or the NOT function.
What function in Microsoft Excel 2003 to write the amount in word?
Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.Such a function does not exist for English. A function call BAHTTEXT will do it for the Thai language.
