# complex fraction

## Definitions

• WordNet 3.6
• n complex fraction a fraction with fractions in the numerator or denominator
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Webster's Revised Unabridged Dictionary
• Complex fraction a fraction having a fraction or mixed number in the numerator or denominator, or in both.
• Complex fraction See Fraction.
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## Usage

### In literature:

Complex and improper fractions and recurring decimals are not allowed.
"Amusements in Mathematics" by Henry Ernest Dudeney
She explained it all to Elizabeth one day, behind their slates, when the complex fraction refused to become simple.
"'Lizbeth of the Dale" by Marian Keith
The village bully is, (as we used to be taught of vulgar fractions) of three kinds, simple, compound, and complex.
"Village Life in China" by Arthur H. Smith
Define a complex fraction.
"A Review of Algebra" by Romeyn Henry Rivenburg
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### In science:

It must be clear that integrals or derivatives of complex order γ ∈ C (and ρ 6= 0) represent an analytic continuation in the parameter γ of fractional integrals and derivatives originally deﬁned for η = Imγ = 0.
On the use of fractional calculus for the probabilistic characterization of random variables
Summing up, in this ﬁrst step we have shown that the classical relation between CF and moments (4) is extended also to complex moments, by the RL deﬁnition of fractional operators.
On the use of fractional calculus for the probabilistic characterization of random variables
The next step is to use a representation of the CF (and of the PDF) in terms of its fractional derivatives of complex order calculated in zero.
On the use of fractional calculus for the probabilistic characterization of random variables
The variance of the number of zeros lying on C In section 3.1 we have established that SI polynomials of the form (3.19) have asymptotically on the average a fraction < ν >= 1/√3 of their roots lying on C if the complex coeﬃcients {ak } are GRIdistributed with the same second moment.
Quantum Chaotic Dynamics and Random Polynomials
Lagrangian is invariant under all M¨obius (linear-fractional) transformations of the complex disk.
q_R-conformal symmetries in 2D nonlocal quantum field theory, categorical representation theory, and Virasoro algebra
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