NationMaster - Encyclopedia: Offset logarithmic integral

The offset logarithmic integral, or European logarithmic integral, is a non-elementary function Li(x) differing by a constant from the logarithmic integral function li(x), defined such that:

Explicitly, this means

where ln is the natural logarithm. It can be shown that

It is often used in formulations of the prime number theorem.

Results from FactBites:

Logarithmic analog-to-digital converter - Patent 4350974 (6178 words)
	Logarithmic converters frequently have advantages over linear converters in applications requiring a very large dynamic range and where the desired accuracy, and hence round-off error, is measured in terms of a specified percentage of the input signal rather than a specified percentage of the maximum output indicated by the converter.
	Since the integral values of x between 1 and 8,192 may be represented by a 13-bit binary number, the logarithm of the input requires only 13 bits for an accuracy of 0.2%, in contrast with the 27 bits required by a linear D/A converter.
	With the inputs to op-amp 56 shorted, the input offset voltage of op-amp 56 is amplified by the open-loop gain of the op-amp, and this amplified offset voltage appears at output terminal 60.

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