# 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 16 subcategories, out of 16 total.

### E

### I

### L

### O

### P

### R

### U

## Pages in category "Reciprocals"

The following 63 pages are in this category, out of 63 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

- Infimum of Set of Reciprocals of Positive Integers
- Integer Reciprocal Space with Zero is not Extremally Disconnected
- Integral of Reciprocal is Divergent
- Integral to Infinity of Reciprocal of Power of x
- Inverse Hyperbolic Cosine of Reciprocal equals Inverse Hyperbolic Secant
- Inverse Hyperbolic Sine of Reciprocal equals Inverse Hyperbolic Cosecant
- Inverse Hyperbolic Tangent of Reciprocal equals Inverse Hyperbolic Cotangent
- Inverse Trigonometric Function of Reciprocal

### N

### P

### R

- Reciprocal as Sum of Fibonacci Numbers by Negative Powers of 10
- Reciprocal as Summation of Binomial Coefficients of Reciprocals
- Reciprocal Function is Strictly Decreasing
- 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 Positive Real Number is Positive
- Reciprocal of Real Exponential
- 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 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 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