Analytic functions are functions that are locally defined by a convergent power series. They are used to compute cumulative, moving, centered, and reporting aggregates. Analytic functions are processed after joins, WHERE clauses, GROUP BY clauses, and HAVING clauses, and can only appear in the select list or ORDER BY clause. Common applications include calculating counts of employees under each manager.

2. Analytic function
• In mathematics , an analyti c function is
a function that is locally given by a convergent
power series . There exist both real analytic
functions and complex analytic
functions, categories that are similar in some
ways, but different in others.
• Functions of each type are infinitely differentiable
, but complex analytic functions exhibit properties
that do not hold generally for real analytic functions

3. • Analytic functions are the last set of
operations performed in a query except for
the final ORDER BY clause. All joins and
all WHERE, GROUP BY, and HAVING
clauses are completed before the analytic
functions are processed. Therefore, analytic
functions can appear only in the select list
or ORDER BY clause.

4. Applications of analytic functions
• Analytic functions are commonly used to
compute cumulative, moving, centered, and
reporting aggregates.
• To calculate employees under each manager

5. • The analytical function provides you the
count(*) of each manager irrespective of the
other column data selected by your query
• Adding a analytical function in your select
clause is just a calculated value apart from
whatever columns you select

6. • Functions of a complex variable provide us
some powerful and widely useful tools in in
theoretical physics.
• Some important physical quantities are
complex variables

7. Complex integration
• Evaluating definite integrals.
• Obtaining asymptotic solutions of differentials
equations. Integral transforms
• Many Physical quantities that were originally
real become complex as simple theory is
made more general. The energy

8. Applications
• These are the famous Cauchy-Riemann
conditions. These Cauchy-Riemann conditions
are necessary for the existence of a
derivative, that is, if exists, the C-R conditions
must hold.
• Conversely, if the C-R conditions are satisfied
and the partial derivatives of u(x,y) and v(x,y)
are continuous,exists.

9. Theorems used in complex
integration
• Cauchy’s integral Theorem
• Laurent Series
We frequently encounter functions that
are analyticin annular region

10. • Taylor Expansion
Suppose we are trying to expand f(z) about z=z
and we have z=z 1 as the nearest point for
which f(z) is not analytic.

11. Thank you all…!!!