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We derive the gluon initiated contribution to the initial condition for theperturbative fragmentation function of a heavy quark through orderO(\alpha_s^2) in the MS-bar scheme. This result is needed for the resummationwith next-to-next-to-leading logarithmic accuracy of quasi-collinear logarithmsln^k(m^2) in heavy quark differential distributions by solving the completeDGLAP equation. Together with the previously evaluated fermion initiatedcomponents, this result completes the derivation of the initial condition forthe perturbative fragmentation function at next-to-next-to-leading order.Comment: 8 pages, 1 figure; minor clarifications in the text; references adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Perturbative heavy quark fragmentation function through<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>α</mml:mi><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math>: Gluon initiated contribution

Perturbative heavy quark fragmentation function throughO(αs2): Gluon initiated contribution