BSI Bessel I
BSI.1 Introduction |
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Let be a complex variable of and let denote a parameter (independent of ).The function Bessel I (noted ) is defined by the following second order differential equation
BSI.1.1 |
Although is a singularity of BSI.1.1, the initial conditions can be given by
BSI.1.2 |
The formulae of this document are valid for
Related function: Bessel K
BSI.2 Series and asymptotic expansions |
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BSI.2.1 Asymptotic expansion at |
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BSI.2.1.2 General form |
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BSI.2.1.2.1 Auxiliary function
The coefficients of satisfy the following recurrence
BSI.2.2 Asymptotic expansion at |
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BSI.2.2.2 General form |
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BSI.2.2.2.1 |
BSI.2.2.2.2 |
BSI.2.2.2.3 |
BSI.2.2.2.4 |