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Hypergeometric0F1Regularized

Hypergeometric0F1Regularized[a, z]
is the regularized confluent hypergeometric function

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

Hypergeometric0F1Regularized[a, z] is finite for all finite values of a and z.

For certain special arguments, Hypergeometric0F1Regularized automatically evaluates to exact values.

Hypergeometric0F1Regularized can be evaluated to arbitrary numerical precision.

Hypergeometric0F1Regularized automatically threads over lists.

EXAMPLES

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Basic Examples (2)

Evaluate numerically:

Series expansion at the origin:

Evaluate numerically:

In[1]:=

Out[1]=

Series expansion at the origin:

In[1]:=

Out[1]=

Scope (6)

Evaluate for complex arguments and parameters:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate symbolically for half-integer parameters:

Hypergeometric0F1Regularized threads element-wise over lists:

TraditionalForm formatting:

Generalizations & Extensions (1)

Series expansion at infinity:

Applications (1)

Probability that in a voting game with 2 candidates, and the number of votes being two independent Poisson random variables with means p and q, candidate 1 gets k more votes than candidate 2 out of n:

Plot distribution for almost even odds:

Neat Examples (1)

Visualize confluence relation