Belevitch used this machine to investigate transcendental functions.
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This directly implies that there exist transcendental functions that produce transcendental numbers only when given transcendental numbers.
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Most familiar transcendental functions, including the special functions of mathematical physics, are solutions of algebraic differential equations.
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As an example of a transcendental function, the logarithm is more familiar than its motivator, the hyperbolic angle.
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A "'transcendental equation "'is an equation containing a transcendental function of the variable ( s ) being solved for.
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Then the natural logarithm could be recognized as the inverse function to the transcendental function e " x ".
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The most familiar transcendental functions are the logarithm, the Bessel functions are transcendental in general, but algebraic for some special parameter values.
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The integrals we have discussed so far involve transcendental functions, but the gamma function also arises from integrals of purely algebraic functions.
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Khovanski? showed that this holds true not just for polynomials but for algebraic combinations of many transcendental functions, the so-called Pfaffian functions.
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But only recently have designers surfed the transcendental functions of the computer's brain to propose curves and forms of formidable complexity and nuance.
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