Пример. Модифицированные функции Бесселя первого рода

Функции > Специальные функции > Функции Бесселя > Пример. Модифицированные функции Бесселя первого рода

Покажите взаимосвязь между функциями I0, I1 и In. Также покажите взаимосвязи между этими функциями и их масштабированными версиями.

1. Определите две переменные определения шага:

2. Постройте графики функций I0 и I1. Добавьте на график функцию второго порядка In:

Щелкните для копирования этого выражения

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3. Постройте график функции In пятого и восьмого порядка:

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• Чем выше порядок функции In, тем более резким становится переход от нуля до бесконечности.

• Только функция I0 имеет свое начало в точке (x=0,y=1). Функции всех остальных порядков имеют начало в точке (x=0,y=0).

4. Создайте график, чтобы показать, что I0(y)=In(0,y). Сбросьте значения делений, чтобы увеличить масштаб по оси X и показать график более подробно:

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5. Создайте график, чтобы показать, что I1(y)=In(1,y). Сбросьте значения делений, чтобы увеличить масштаб по оси X и показать график более подробно:

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6. Используйте аналитические преобразования, чтобы показать взаимосвязь между каждой функцией и ее масштабированной версией:

7. Создайте график, чтобы показать, что:

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У модифицированных функций Бесселя первого рода нет пиков.

Было ли это полезно?