Setting upper limits on the strength of periodic gravitational waves from PSR<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">J</mml:mi><mml:mn>1</mml:mn><mml:mn>9</mml:mn><mml:mn>3</mml:mn><mml:mn>9</mml:mn><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mn>1</mml:mn><mml:mn>3</mml:mn><mml:mn>4</mml:mn></mml:math>using the first science data from the GEO 600 and LIGO detectors

Data collected by the GEO 600 and LIGO interferometric gravitational wave detectors during their first observational science run were searched for continuous gravitational waves from the pulsar $\mathrm{J}1939+2134$ at twice its rotation frequency. Two independent analysis methods were used and are demonstrated in this paper: a frequency domain method and a time domain method. Both achieve consistent null results, placing new upper limits on the strength of the pulsar's gravitational wave emission. A model emission mechanism is used to interpret the limits as a constraint on the pulsar's equatorial ellipticity.