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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=5, b₁>=-11/2

For fixed z and a₁=7/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{7/2, 5}, {-(9/2), 3/2}, z] == (1/42525) (42525 - 110250 z + 170100 z^2 - 249480 z^3 + 480480 z^4 - 2358720 z^5 - 3227280 z^6 - 1343680 z^7 - 249774 z^8 - 22756 z^9 - 984 z^10 - 16 z^11) - (1/42525) (E^z Sqrt[Pi] z^(11/2) (3527160 + 3798480 z + 1458345 z^2 + 260680 z^3 + 23240 z^4 + 992 z^5 + 16 z^6) 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]