## Interpolating functions associated with second-order differential equations

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- by William F. Trench PDF
- Proc. Amer. Math. Soc.
**78**(1980), 253-258 Request permission

## Abstract:

Functions are exhibited which interpolate the magnitude of a solution*y*of a linear, homogeneous, second-order differential equation at its critical points, $|y’|$ at the zeros of

*y*, and $|\smallint _{{x_0}}^xy(t)h(t)\;dt|$ at the zeros of

*y*. Except for a normalization condition, the interpolating functions are independent of the specific solution

*y*. A theorem similar in its conclusions to the Sonin-Pólya-Butlewski theorem is presented and examples are given.

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## Additional Information

- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**78**(1980), 253-258 - MSC: Primary 34C10; Secondary 33A40, 34B25
- DOI: https://doi.org/10.1090/S0002-9939-1980-0550507-9
- MathSciNet review: 550507