# HASN.1 Introduction

Let be a complex variable of .The function Inverse Hyperbolic Sine (noted ) is defined by the following second order differential equation

HASN.1.1

The initial conditions of HASN.1.1 are given at by

 HASN.1.2

# HASN.2 Series and asymptotic expansions

## HASN.2.1 Asymptotic expansion at

### HASN.2.1.1 First terms

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 HASN.2.1.1.1

### HASN.2.1.2 General form

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The general form of is not easy to state and requires to exhibit the basis of formal solutions of ?? (coming soon).

## HASN.2.2 Asymptotic expansion at

### HASN.2.2.1 First terms

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 HASN.2.2.1.1

### HASN.2.2.2 General form

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The general form of is not easy to state and requires to exhibit the basis of formal solutions of ?? (coming soon).

## HASN.2.3 Taylor expansion at

HASN.2.3.1.1

### HASN.2.3.2 General form

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 HASN.2.3.2.1
The coefficients satisfy the recurrence
HASN.2.3.2.2
Initial conditions of HASN.2.3.2.2 are given by
HASN.2.3.2.3

## HASN.2.4 Asymptotic expansion at

### HASN.2.4.1 First terms

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 HASN.2.4.1.1

### HASN.2.4.2 General form

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The general form of is not easy to state and requires to exhibit the basis of formal solutions of ?? (coming soon).

# HASN.3 Graphs

## HASN.3.1 Real axis

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## HASN.3.2 Complex plane

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