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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(11/2), -(7/2)}, z] == (1/3094331625) (E^z (3094331625 - 884094750 z + 1571724000 z^2 + 3143448000 z^3 + 40864824000 z^4 - 779994230400 z^5 + 13661844134400 z^6 + 130864674124800 z^7 + 269981188646400 z^8 + 232909578316800 z^9 + 103971448627200 z^10 + 26633830809600 z^11 + 4133686394880 z^12 + 398023557120 z^13 + 23712890880 z^14 + 843841536 z^15 + 16318464 z^16 + 131072 z^17))

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]