Holzmark functions H(β), G(β), and average lifespan τ(β)
Author: tonagaiExecutions: 138
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When stars are randomly distributed in three dimensions, the Holtzmark distribution describes the distribution observed at a single point under the influence of their gravity.
H(β) = (2/πβ)∫exp(-(x/β)^(3/2)) * x * sin(x) dx,
G(β) = (2/π)∫exp(-(x/β)^(3/2)) * sin(x)/√x dx,
τ(β) = √β^(3/2) * H(β)/G(β)
are calculated using the double exponential integral formula.
G(β) = (2/π)∫exp(-(x/β)^(3/2)) * sin(x)/√x dx,
τ(β) = √β^(3/2) * H(β)/G(β)
are calculated using the double exponential integral formula.
| β | |
| H(β) | |
| G(β) | |
| Life expectancy τ(β) |
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