# LameCPrime LameCPrime[ν,j,z,m]

gives the -derivative of the  Lamé function of order with elliptic parameter .

# Details • Mathematical function, suitable for both symbolic and numerical manipulation.
• LameCPrime belongs to the Lamé class of functions.
• For certain special arguments, LameCPrime automatically evaluates to exact values.
• LameCPrime can be evaluated to arbitrary numerical precision for an arbitrary complex argument.
• LameCPrime automatically threads over lists.
• LameCPrime[ν,0,z,0]=0 and LameCPrime[ν,j,z,0]=j Sin[j( -z)].

# Examples

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## Basic Examples(3)

Evaluate numerically:

Plot the LameCPrime function for and :

Series expansion of LameCPrime at the origin:

## Scope(23)

### Numerical Evaluation(5)

Evaluate to high precision:

The precision of the output tracks the precision of the input:

LameCPrime can take complex number parameters and argument:

Evaluate LameCPrime efficiently at high precision:

Lists and matrices:

### Specific Values(1)

Value of LameCPrime when and :

Value of LameCPrime when and :

### Visualization(6)

Plot the first three even LameCPrime functions:

Plot the first three odd LameCPrime functions:

Plot the absolute value of the LameCPrime function for complex parameters:

Plot LameCPrime as a function of its first parameter :

Plot LameCPrime as a function of and elliptic parameter :

Plot the family of LameCPrime functions for different values of the elliptic parameter :

### Function Properties(2)

When is even, LameCPrime is a periodic function of real argument with a period 2EllipticK[m] and has an initial value LameCPrime[ν,j,0,m]=0:

When is odd, LameCPrime is a periodic function of real argument with a period 4EllipticK[m]:

### Differentiation(2)

The -derivative of LameCPrime involves LameC function:

Derivatives of LameCPrime for specific cases of parameters:

### Integration(3)

Indefinite integral of LameCPrime is LameC:

Definite numerical integrals of LameCPrime:

More integrals with LameCPrime:

### Series Expansions(3)

Series expansion of LameCPrime at the origin:

Coefficient of the second term of this expansion:

Plot the first- and third-order approximations for LameCPrime around :

Series expansion for LameCPrime at any ordinary complex point:

### Function Representations(1)

LameCPrime cannot be represented in terms of MeijerG:

## Applications(1)

Use the LameCPrime function to calculate the derivatives of LameC:

## Properties & Relations(1)

LameCPrime is an even function when is a positive odd integer:

LameCPrime is an odd function when is a non-negative even integer:

## Possible Issues(1)

LameCPrime is not defined if is a negative integer:

LameCPrime is not defined if is not an integer: