What is the meaning of True in my result? [closed]What is the principal difference betwen two results of a seemingly similar sums?Question about sum and list in a functionProblem evaluating a complicated integralSumConvergence[((-1)^n)/(Sqrt[n] + (-1)^n), n] returns True in Version 10.2?Infinite Sum: $sum_k (ak^2+bk+c)^-1$Numerical result using summation limitLeave Kronecker deltas unevaluatedReturn analytic expressionComputing numerically infinite sum of some double seriesEfficiently define a function as the numerical result of infinite sumsWhy is the result of a Cesaro regularized sum dependant on a mathematically redundant parameter?

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What is the meaning of True in my result? [closed]

What is the principal difference betwen two results of a seemingly similar sums?Question about sum and list in a functionProblem evaluating a complicated integralSumConvergence[((-1)^n)/(Sqrt[n] + (-1)^n), n] returns True in Version 10.2?Infinite Sum: $sum_k (ak^2+bk+c)^-1$Numerical result using summation limitLeave Kronecker deltas unevaluatedReturn analytic expressionComputing numerically infinite sum of some double seriesEfficiently define a function as the numerical result of infinite sumsWhy is the result of a Cesaro regularized sum dependant on a mathematically redundant parameter?

When I do the sum

Sum[(a + (b + π n)^2)^(-1), n, -∞, ∞]

the result reads

$$beginarraycc
{ &
beginarraycc
fraccoth left(sqrta+i bright)+coth left(sqrta-i bright)2 sqrta & arg left(sqrta-i bright)geq -fracpi 2land arg left(sqrta-i bright)leq fracpi 2 \
fraccoth left(sqrta+i bright)2 sqrta+fraccoth left(sqrta-i bright)2 sqrta-frac1sqrta & textTrue \
endarray
\
endarray
$$

What is the meaning of True in the second result?

If I get rid of $pi$, the result is simply:

$$ frac-pi cot left(pi sqrt-a+pi bright)-pi cot left(pi sqrt-a-pi bright)2 sqrt-a$$

edited May 23 at 13:13

m_goldberg

90.5k873203

asked May 22 at 18:40

wondering

295113

closed as off-topic by Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB May 23 at 14:15

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment |

When I do the sum

Sum[(a + (b + π n)^2)^(-1), n, -∞, ∞]

the result reads

What is the meaning of True in the second result?

If I get rid of $pi$, the result is simply:

$$ frac-pi cot left(pi sqrt-a+pi bright)-pi cot left(pi sqrt-a-pi bright)2 sqrt-a$$

edited May 23 at 13:13

m_goldberg

90.5k873203

asked May 22 at 18:40

wondering

295113

closed as off-topic by Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB May 23 at 14:15

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment |

When I do the sum

Sum[(a + (b + π n)^2)^(-1), n, -∞, ∞]

the result reads

What is the meaning of True in the second result?

If I get rid of $pi$, the result is simply:

$$ frac-pi cot left(pi sqrt-a+pi bright)-pi cot left(pi sqrt-a-pi bright)2 sqrt-a$$

edited May 23 at 13:13

m_goldberg

90.5k873203

asked May 22 at 18:40

wondering

295113

When I do the sum

Sum[(a + (b + π n)^2)^(-1), n, -∞, ∞]

the result reads

What is the meaning of True in the second result?

If I get rid of $pi$, the result is simply:

$$ frac-pi cot left(pi sqrt-a+pi bright)-pi cot left(pi sqrt-a-pi bright)2 sqrt-a$$

summation

edited May 23 at 13:13

m_goldberg

90.5k873203

asked May 22 at 18:40

wondering

295113

edited May 23 at 13:13

m_goldberg

90.5k873203

asked May 22 at 18:40

wondering

295113

edited May 23 at 13:13

m_goldberg

90.5k873203

edited May 23 at 13:13

m_goldberg

90.5k873203

edited May 23 at 13:13

m_goldberg

90.5k873203

asked May 22 at 18:40

wondering

295113

asked May 22 at 18:40

wondering

295113

asked May 22 at 18:40

wondering

295113

closed as off-topic by Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB May 23 at 14:15

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB May 23 at 14:15

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment |

1 Answer
1

active

oldest

votes

See Piecewise. It is like the cases environment in $LaTeX$. In native math, one would use "else" instead of True.

By the way, version 12 returns

$$begincases
fraccoth left(sqrta-i bright)+coth left(sqrta+i
bright)2 sqrta & arg left(b+i sqrtaright)geq 0 \
fraccoth left(sqrta-i bright)2 sqrta+fraccoth
left(sqrta+i bright)2 sqrta-frac1sqrta &
textTrue
endcases$$

to be interpreted as

answered May 22 at 18:43

Henrik Schumacher

63.8k590178

1

$begingroup$
Ok, so it really simply means "otherwise" or "else" or "in all other cases"?
$endgroup$
– wondering
May 22 at 18:44

$begingroup$
Yes. That is correct.
$endgroup$
– Henrik Schumacher
May 22 at 18:45

add a comment |

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

See Piecewise. It is like the cases environment in $LaTeX$. In native math, one would use "else" instead of True.

By the way, version 12 returns

to be interpreted as

answered May 22 at 18:43

Henrik Schumacher

63.8k590178

1

$begingroup$
Ok, so it really simply means "otherwise" or "else" or "in all other cases"?
$endgroup$
– wondering
May 22 at 18:44

$begingroup$
Yes. That is correct.
$endgroup$
– Henrik Schumacher
May 22 at 18:45

add a comment |

See Piecewise. It is like the cases environment in $LaTeX$. In native math, one would use "else" instead of True.

By the way, version 12 returns

to be interpreted as

answered May 22 at 18:43

Henrik Schumacher

63.8k590178

1

$begingroup$
Ok, so it really simply means "otherwise" or "else" or "in all other cases"?
$endgroup$
– wondering
May 22 at 18:44

$begingroup$
Yes. That is correct.
$endgroup$
– Henrik Schumacher
May 22 at 18:45

add a comment |

See Piecewise. It is like the cases environment in $LaTeX$. In native math, one would use "else" instead of True.

By the way, version 12 returns

to be interpreted as

answered May 22 at 18:43

Henrik Schumacher

63.8k590178

See Piecewise. It is like the cases environment in $LaTeX$. In native math, one would use "else" instead of True.

By the way, version 12 returns

to be interpreted as

answered May 22 at 18:43

Henrik Schumacher

63.8k590178

answered May 22 at 18:43

Henrik Schumacher

63.8k590178

answered May 22 at 18:43

Henrik Schumacher

63.8k590178

answered May 22 at 18:43

Henrik Schumacher

63.8k590178

1

$begingroup$
Ok, so it really simply means "otherwise" or "else" or "in all other cases"?
$endgroup$
– wondering
May 22 at 18:44

$begingroup$
Yes. That is correct.
$endgroup$
– Henrik Schumacher
May 22 at 18:45

add a comment |

1

$begingroup$
Ok, so it really simply means "otherwise" or "else" or "in all other cases"?
$endgroup$
– wondering
May 22 at 18:44

$begingroup$
Yes. That is correct.
$endgroup$
– Henrik Schumacher
May 22 at 18:45

Ok, so it really simply means "otherwise" or "else" or "in all other cases"?

– wondering
May 22 at 18:44

Yes. That is correct.

– Henrik Schumacher
May 22 at 18:45

add a comment |

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closed as off-topic by Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB May 23 at 14:15

closed as off-topic by Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB May 23 at 14:15

closed as off-topic by Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB May 23 at 14:15

closed as off-topic by Bob Hanlon, Carl Lange, m_goldberg, Daniel Lichtblau, MarcoB May 23 at 14:15

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