# Category:Reciprocals

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This category contains results about Reciprocals.

Definitions specific to this category can be found in Definitions/Reciprocals.

Let $x \in \R$ be a real number such that $x \ne 0$.

Then $\dfrac 1 x$ is called the **reciprocal of $x$**.

## Subcategories

This category has the following 23 subcategories, out of 23 total.

### E

- Examples of Reciprocals (35 P)

### I

- Integer Reciprocal Space (13 P)

### L

### O

- Ordering of Reciprocals (3 P)

### P

- Primitive of Reciprocal (4 P)

### R

- Reciprocal of Logarithm (3 P)
- Reciprocal of Null Sequence (2 P)

### S

### U

## Pages in category "Reciprocals"

The following 80 pages are in this category, out of 80 total.

### A

- Approximation to Reciprocal times Derivative of Gamma Function
- Arccosecant of Reciprocal equals Arcsine
- Arccosine of Reciprocal equals Arcsecant
- Arccotangent of Reciprocal equals Arctangent
- Arcsecant of Reciprocal equals Arccosine
- Arcsine of Reciprocal equals Arccosecant
- Arctangent of Reciprocal equals Arccotangent

### C

### I

### L

### M

### N

- Newton-Mercator Series/Examples/2
- Nth Derivative of Reciprocal
- Nth Derivative of Reciprocal of Mth Power
- Nth Derivative of Reciprocal of Mth Power/Corollary
- Number times Recurring Part of Reciprocal gives 9-Repdigit
- Number to Reciprocal Power is Decreasing
- Numbers the Multiple of whose Reciprocal are Cyclic Permutations

### P

### R

- Rational Number Expressible as Sum of Reciprocals of Distinct Squares
- Real Area Hyperbolic Cosine of Reciprocal equals Real Area Hyperbolic Secant
- Real Area Hyperbolic Sine of Reciprocal equals Real Area Hyperbolic Cosecant
- Real Area Hyperbolic Tangent of Reciprocal equals Real Area Hyperbolic Cotangent
- Reciprocal as Sum of Fibonacci Numbers by Negative Powers of 10
- Reciprocal as Summation of Binomial Coefficients of Reciprocals
- Reciprocal Function is Continuous on Real Numbers without Zero
- Reciprocal Function is Discontinuous at Zero
- Reciprocal Function is Strictly Decreasing
- Reciprocal Function is Unbounded on Open Unit Interval
- Reciprocal of Complex Exponential
- Reciprocal of Holomorphic Function
- Reciprocal of Logarithm
- Reciprocal of Null Sequence
- Reciprocal of One Minus Secant
- Reciprocal of One Plus Cosecant
- Reciprocal of Quotient of Real Numbers
- Reciprocal of Real Exponential
- Reciprocal of Real Number is Non-Zero
- Reciprocal of Square of 1 Less than Number Base
- Reciprocal of Strictly Negative Real Number is Strictly Negative
- Reciprocal of Strictly Positive Real Number is Strictly Positive
- Reciprocal Sequence is Strictly Decreasing
- Reciprocals of Odd Numbers adding to 1
- Reciprocals whose Decimal Expansion contain Equal Numbers of Digits from 0 to 9

### S

- Sequence of Powers of Reciprocals is Null Sequence
- Sequence of Reciprocals is Null Sequence
- Sequence of Smallest Numbers whose Reciprocal has Period n
- Sum of Reciprocals in Base 10 with Zeroes Removed
- Sum of Sequence of Products of 3 Consecutive Reciprocals
- Sum of Sequence of Products of 3 Consecutive Reciprocals/Corollary
- Sum of Sequence of Products of Consecutive Odd and Consecutive Even Reciprocals
- Sum of Sequence of Products of Consecutive Odd and Consecutive Even Reciprocals/Corollary
- Sum of Sequence of Products of Consecutive Odd Reciprocals
- Sum of Sequence of Products of Consecutive Odd Reciprocals/Corollary
- Sum of Sequence of Products of Consecutive Reciprocals
- Sum of Sequence of Products of Squares of 3 Consecutive Reciprocals
- Sum of Sequence of Products of Squares of 3 Consecutive Reciprocals/Proof 1
- Sum of Sequence of Products of Squares of 3 Consecutive Reciprocals/Proof 2
- Sum of Sequence of Products of Squares of Consecutive Odd Reciprocals
- Sum of Sequence of Reciprocals of 3 n + 1 Alternating in Sign
- Sum of Sequence of Reciprocals of 3 n + 2 Alternating in Sign
- Sum of Sequence of Reciprocals of 4 n + 1 Alternating in Sign