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

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=5/2, a₂>=5/2

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

For fixed z and a₁=5/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{5/2, 5}, {-(9/2), -(3/2)}, z] == (1/25515) (25515 + 47250 z + 283500 z^2 - 2381400 z^3 + 11642400 z^4 - 108972864 z^5 - 355118400 z^6 - 313915200 z^7 - 122698656 z^8 - 24819168 z^9 - 2756600 z^10 - 167952 z^11 - 5216 z^12 - 64 z^13) - (1/25515) (4 E^z Sqrt[Pi] (52907400 z^(11/2) + 118024200 z^(13/2) + 91407708 z^(15/2) + 33479292 z^(17/2) + 6529929 z^(19/2) + 709512 z^(21/2) + 42632 z^(23/2) + 1312 z^(25/2) + 16 z^(27/2)) 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]