Jν⁡(z)=1π⁢∫0πcos⁡(z⁢sin⁡θ-ν⁢θ)⁢ⅆ⁡θ-sin⁡(ν⁢π)π⁢∫0∞ⅇ-z⁢sinh⁡t-ν⁢t⁢ⅆ⁡t,