Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ane9)

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=5, a₂>=5

For fixed z and a₁=5, a₂=11/2, b₁>=-11/2

For fixed z and a₁=5, a₂=11/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.ane9.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(5/2), 3/2}, z] == (1/42525) (42525 - 311850 z + 1621620 z^2 - 16216200 z^3 - 57657600 z^4 - 55036800 z^5 - 23073120 z^6 - 4978944 z^7 - 587310 z^8 - 37860 z^9 - 1240 z^10 - 16 z^11) - (1/42525) (E^z Sqrt[Pi] z^(7/2) (32432400 + 77837760 z + 64668240 z^2 + 25310880 z^3 + 5255145 z^4 + 605640 z^5 + 38472 z^6 + 1248 z^7 + 16 z^8) 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]