The Rayleigh-Jeans law is a formula that approximates black-body radiation at longer wavelengths, i.e., approximates one of the two tails of the spectrum, which is precisely specified by the Planck function. The Raleigh-Jeans law has the advantage of being a simpler function, easier to manipulate algebraically and incorporate into formulae describing astronomical phenomena.
Bλ(T) = 2cKBT/λ4
Or, based upon frequency, giving a SED according to frequency-differentials:
Bν(T) = 2ν²KBT/c²
Being a good approximation of the spectrum's longer-wavelength tail, it is useful in radio astronomy. The region of the spectrum where it is a useful approximation is called the Rayleigh-Jeans regime or Raleigh-Jeans region. The this regime's location depends upon the temperature-regime: the hotter the type of objects, the more the Rayleigh-Jeans regime extends toward shorter wavelengths.
The Rayleigh-Jeans law was devised before the Planck function was known and was derived from classical (pre-quantum mechanics) physical principles by Lord Rayleigh and James Jeans. However, it was clearly wrong: it says that the shorter the wavelength, the more electromagnetic radiation is emitted at that wavelength, approaching infinity. Among other issues, this implies objects would cool to zero in zero time. This anomaly between theory and observation was termed the ultraviolet catastrophe. The Planck function matched observation and quantum mechanics developed from the physical rules this implied. Toward longer wavelengths, the Planck function approaches the Raleigh-Jeans law's formula, and the formula is in some situations referred to as the Rayleigh-Jeans limit.