Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ac4y)

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=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=5, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.ac4y.01

Input Form

HypergeometricPFQ[{-(1/2), 5}, {-(11/2), 5/2}, z] == (37800 - 5040 z - 12600 z^2 + 9000 z^3 - 3375 z^4 + 855 z^5 - 126 z^6 - 116 z^7 - 8 z^8)/(83160 z) + (1/(166320 z^(3/2))) (E^z Sqrt[Pi] (-37800 + 113400 z - 37800 z^2 - 12600 z^3 + 14175 z^4 - 5985 z^5 + 1680 z^6 - 360 z^7 - 240 z^8 - 16 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]