##  [Gibbs Phenomenon](/gibbs-phenomenon) 

  ##  [Gibbs Phenomenon](https://natural.quantumdictionary.io/gibbs-phenomenon-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The persistent overshoot and oscillatory ringing near a jump discontinuity that occurs when approximating a piecewise‑smooth function by truncated Fourier series or other global spectral expansions; the overshoot does not vanish as the number of terms grows, although it narrows.

 

 

 

 

 





 

 



 ##  [Gibbs Phenomenon](https://mathlogic.quantumdictionary.io/gibbs-phenomenon-1) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The persistent oscillatory overshoot and ringing that occur near a jump discontinuity when a function is approximated by a truncated global series or spectral expansion (e.g., Fourier series); the overshoot approaches a finite fraction of the jump and does not vanish with truncation number.