# tf.math.special.spence

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| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v2.13.1/tensorflow/python/ops/special_math_ops.py#L222-L249) |

Computes Spence's integral of `x` element-wise.

#### View aliases


**Compat aliases for migration**

See
[Migration guide](https://www.tensorflow.org/guide/migrate) for
more details.

[`tf.compat.v1.math.special.spence`](https://www.tensorflow.org/api_docs/python/tf/math/special/spence)

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    tf.math.special.spence(
        x, name=None
    )

Spence's integral is defined as the integral of `log(t) / (1 - t)` from
`1` to `x`, with the domain of definition all non-negative real numbers.

    tf.math.special.spence([0.5, 1., 2., 3.]).numpy()
    array([ 0.58224034,  0.        , -0.82246685, -1.4367464], dtype=float32)

This implementation is based off of the Cephes math library.

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| ## Args ||
|---|---|
| `x` | A `Tensor` or `SparseTensor`. Must be one of the following types: `float32`, `float64`. |
| `name` | A name for the operation (optional). |

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| ## Returns ||
|---|---|
| A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. ||

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## scipy compatibility

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Equivalent to scipy.special.spence

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