recurrence relation

Examples of recurrence relation in the following topics:

• Series Solutions

  • In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
  • After substituting the power series form, recurrence relations for $A_k$ is obtained, which can be used to reconstruct $f$.
  • We can rearrange this to get a recurrence relation for $A_{k+2}$:
  • and all coefficients with larger indices can be similarly obtained using the recurrence relation.

• Counting Rules and Techniques

  • It involves the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their properties.
  • Generating functions and recurrence relations are powerful tools that can be used to manipulate sequences, and can describe if not resolve many combinatorial situations.
  • A recurrence relation defines each term of a sequence in terms of the preceding terms.
  • The Fibonacci sequence is one example of a recurrence relation.

• Theoretical Probability

  • It can also be obtained recursively through the Fibonacci recurrence relation.

• Vulvovaginal Candidiasis

  • During pregnancy, the Candida fungus is more prevalent (common), and recurrent infection is also more likely.
  • Frequency of sexual intercourse appears to be related to the frequency of infections, however infections often occur without sex.

• Panic Disorder and Panic Attacks

  • People with panic disorder experience recurrent (more than one) and unexpected panic attacks, along with at least one month of persistent concern about additional panic attacks, worry over the consequences of the attacks, or self-defeating changes in behavior related to the attacks (such as withdrawing from social activities out of fear of having an attack) (APA, 2013).
  • In order to be diagnosed with panic disorder, a person must experience unexpected, recurrent panic attacks.
  • These panic attacks must also be accompanied by at least one month of a significant and related behavior change in relation to the attacks, a persistent concern or fear of more attacks, or a worry about the attacks' consequences.

• Medical Imaging and Diagnostics

  • The nuclear medicine whole body bone scan is generally used in evaluations of various bone related pathology, such as for bone pain, stress fracture, nonmalignant bone lesions, bone infections, or the spread of cancer to the bone.
  • It may also be used as part of curative therapy, to prevent tumor recurrence after surgery, or to remove a primary malignant tumor.

• Functions of the Cerebellum

  • Functional imaging studies have also shown cerebellar activation in relation to language, attention, and mental imagery.
  • This means signals move unidirectionally through the system from input to output with very little recurrent internal transmission.
  • The small amount of recurrence that does exist consists of mutual inhibition.

• Syncope

  • Other types include postural syncope (caused by a change in body posture), cardiac syncope (due to heart-related conditions), and neurological syncope (due to neurological conditions).
  • Recurrent syncope with complex associated symptoms called neurally mediated syncope.

• Pancreatic Islet Disorders: Diabetes and Hyperinsulinism

  • Normal insulin secretion and blood levels are closely related to the level of glucose in the blood, so that a given level of insulin can be normal for one blood glucose level but low or high for another.
  • Recurrent hypoglycemia may be prevented by reversing or removing the underlying cause, by increasing the frequency of meals, with medications like diazoxide, octreotide, or glucocorticoids, or by surgical removal of much of the pancreas.

• Bipolar Disorders

  • The "bipolar spectrum" refers to the range in which these alternating moods may occur and includes bipolar I, bipolar II, cyclothymia, and other specified bipolar and related disorder.
  • A psychiatric mood disorder in children, it is characterized by persistently irritable or angry mood with recurrent, severe temper outbursts.
  • Psychotherapy is aimed at alleviating core symptoms, recognizing episode triggers, reducing negative expressed emotion in relationships, recognizing symptoms before full-blown recurrence, and practicing the factors that lead to maintenance of remission.