Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anc3)

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=-11/2

http://functions.wolfram.com/07.25.03.anc3.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(11/2), 3/2}, z] == (1/29469825) (29469825 - 98232750 z + 170270100 z^2 - 243243000 z^3 + 367567200 z^4 - 761866560 z^5 + 4102358400 z^6 + 6876334080 z^7 + 3716254080 z^8 + 970200000 z^9 + 139051968 z^10 + 11426160 z^11 + 532512 z^12 + 12992 z^13 + 128 z^14) + (1/29469825) (8 E^z Sqrt[Pi] z^(13/2) (805820400 + 1047566520 z + 517989780 z^2 + 129327660 z^3 + 18064305 z^4 + 1460760 z^5 + 67368 z^6 + 1632 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]