6.10 If we integrate the Maxwell-Boltzmann distribution over from some momentum up, we are faced with...

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6.10 If we integrate the Maxwell-Boltzmann distribution over from some momentum up, we are faced with error functions 00 2 erfc(y) = = 7/7 S, dr. d.x. Problems 87 [See Handbook of Mathematical Functions, M. Abramowitz and L.A. Stegun, Eds. (National Bureau of Standards, 1964).] (0) Show the following asymptotic behavior for large y [+] RIG- 2y 4 8 dxo- 31 (Hint: Transform to new integration variable. The asymptotic behavior of the integral fa dt 1/2 e can be obtained by repeated partial integrations.) (b) Differentiate , dxe with respect to A, and then set =1, to obtain the asymptotic formulas 00 dxxe-- -(+1/2). 2y dxx0 (++3/4). 63 2y 6.10 If we integrate the Maxwell-Boltzmann distribution over from some momentum up, we are faced with error functions 00 2 erfc(y) = = 7/7 S, dr. d.x. Problems 87 [See Handbook of Mathematical Functions, M. Abramowitz and L.A. Stegun, Eds. (National Bureau of Standards, 1964).] (0) Show the following asymptotic behavior for large y [+] RIG- 2y 4 8 dxo- 31 (Hint: Transform to new integration variable. The asymptotic behavior of the integral fa dt 1/2 e can be obtained by repeated partial integrations.) (b) Differentiate , dxe with respect to A, and then set =1, to obtain the asymptotic formulas 00 dxxe-- -(+1/2). 2y dxx0 (++3/4). 63 2y

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