Integrate a Hermite series and multiply the result by a scalar before the integration constant is added in Python

To integrate a Hermite series and multiply the result by a scalar before adding the integration constant, use the hermite.hermint() method in Python. This function provides control over the integration process through several parameters including the scalar multiplier.

Syntax

hermite.hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0)

Parameters

The key parameters for scalar multiplication during integration are ?

• c ? Array of Hermite series coefficients
• m ? Order of integration (default: 1)
• k ? Integration constant(s) (default: [])
• lbnd ? Lower bound of integral (default: 0)
• scl ? Scalar multiplier applied before adding integration constant (default: 1)
• axis ? Axis over which integral is taken (default: 0)

Example

Let's integrate a Hermite series with a scalar multiplier of -2 ?

import numpy as np
from numpy.polynomial import hermite as H

# Create an array of coefficients
c = np.array([1, 2, 3])

# Display the array
print("Our Array...")
print(c)

# Check the dimensions and properties
print("\nDimensions of our Array...")
print(c.ndim)

print("\nDatatype of our Array object...")
print(c.dtype)

print("\nShape of our Array object...")
print(c.shape)

# Integrate Hermite series with scalar multiplication
print("\nResult...")
print(H.hermint(c, scl=-2))

Our Array...
[1 2 3]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(3,)

Result...
[-2. -1. -1. -1.]

How It Works

The scl parameter multiplies the integrated result by the specified scalar before adding the integration constant. In the example above, each coefficient is integrated and then multiplied by -2, producing the final result [-2. -1. -1. -1.].

Comparison of Different Scalar Values

Conclusion

The hermite.hermint() function with the scl parameter allows you to integrate Hermite series and apply scalar multiplication before adding integration constants. This provides flexibility in mathematical operations involving Hermite polynomials.