Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9e1)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.a9e1.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(5/2), 23/4}, -z] == (209 (Sqrt[Pi] (-23609013553125 - 6078642570000 z - 1060999430400 z^2 - 192471552000 z^3 - 60383232000 z^4 + 44590694400 z^5 - 5284823040 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-7869671184375 + 1571349780000 z - 8821612800 z^2 - 4474552320 z^3 + 2855731200 z^4 - 333447168 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (23609013553125 - 19104305220000 z + 972783302400 z^2 - 8159477760 z^3 + 3158507520 z^4 - 346030080 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/(16492674416640 z^(19/4))

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]