Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4908)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=4, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=4, b₁=2

http://functions.wolfram.com/07.25.03.4908.01

Input Form

HypergeometricPFQ[{-(9/2), 4}, {2, 11/2}, -z] == (1/(25165824 z^4)) ((-496125 - 75600 z + 173880 z^2 + 756000 z^3 + 16110912 z^4 + 15725568 z^5 + 4555392 z^6 + 485888 z^7 + 16640 z^8)/ E^z) + (1/(50331648 z^(9/2))) (Sqrt[Pi] (496125 - 255150 z - 136080 z^2 - 635040 z^3 + 9525600 z^4 + 44452800 z^5 + 35562240 z^6 + 9580032 z^7 + 988416 z^8 + 33280 z^9) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]