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WAVEPARTITION FUNCTIONS O1G3t Oilbi
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addition of velocities addition rule analysis analytic functions angular momentum operator approximately bipolar geometry Bose-Einstein chapter charge charge-pair model chemical potential commutation rules complex variables considered corresponding cosech density matrix derivatives describe differential equation Doppler effect eigenvalue electromagnetic electrostatic elliptic functions elliptic integral examined expressed factor Fermi-Dirac fimctions fluctuations Fourier series free energy give grand canonical potential grand partition function Hence homography hyperbolic tangent inertial frames infinite product infinite product representation interaction Jacobi Laplace transform logarithm motion notation obtained optical effects particle phase changes photon flow photon traffic physical theory Planck’s radiation law potential coefficients previous section propagation properties pure imaginary q-series quantization quantum numbers quantum theory Schroedinger equation seen sigma functions sn-function special relativity statistical mechanics surfaces tanh theory of special thermodynamic theta and sigma theta functions typical term vacuum values wave functions Weierstrass zero zeta