[A new method for calculating a compensation function in power series].

Area of Science:

• Power series analysis
• Mathematical modeling

Context:

• Traditional methods for deriving compensation functions often rely on logarithmic linear regression.
• Limitations exist in computational requirements and accuracy for certain datasets.

Purpose:

• To introduce a novel power series method for compensation function derivation.
• To compare its performance against logarithmic linear regression.
• To derive new formulas for power series regression without logarithms.

Summary:

• A new power series method, termed the "persistence report," is developed for compensation function derivation.
• This method is compared to logarithmic linear regression, showing often superior approximation of measured values.
• New, simpler formulas for power series regression, usable without computers, are also derived.

Impact:

• Provides a more accurate and accessible method for compensation function analysis.
• Simplifies regression calculations, potentially reducing computational costs.
• Offers a viable alternative for applications where computer access is limited.