Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

Metadata 
bibkey: nist2026dlmfbesselkintegral
authors: NIST Digital Library of Mathematical Functions
year: 2026
title: Modified Bessel functions, integral representations
doi: 10.18434/T4J30S
url: https://dlmf.nist.gov/10.32.E9
claim: "DLMF 10.32.9 gives the hyperbolic integral representation of the modified Bessel function K."
strata_touched:
  - D5/S3/Analytic/GammaGammaNBU/Result
  - D5/S3/Analytic/GauntBesselTail/Result
license: citation-only
triage: anchor

Modified Bessel K as a hyperbolic integral

Verified locator

https://dlmf.nist.gov/10.32.E9

DOI: 10.18434/T4J30S.

Equation 10.32.9:

K_ν(z) = ∫_0^∞ exp(−z cosh t) cosh(νt) dt, |ph z| < ½π

For real and real the integral is real. In particular, .