Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8443)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8443.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(7/4)}, -z] == (2 Sqrt[z] (-14230536445125 - 542115674100 z - 1700755056000 z^2 + 618007864320 z^3 - 291768238080 z^4 + 430842839040 z^5 + 51228868608 z^6 + 1330642944 z^7 + 8388608 z^8) Cos[2 Sqrt[z]] + 32768 Sqrt[Pi] z^(25/4) (232105995 + 25611696 z + 653568 z^2 + 4096 z^3) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (-14230536445125 + 18431932919400 z + 4081812134400 z^2 - 2093236992000 z^3 + 784114974720 z^4 - 566018703360 z^5 + 3728367157248 z^6 + 417641791488 z^7 + 10695475200 z^8 + 67108864 z^9) Sin[2 Sqrt[z]])/(14198385801600 z^(7/2))

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]